Have a query? Ask a Tutor!!

Access to best educators and exclusive paper discussions

Offsite Campus Turito Championship

Can’t find what you’re looking for?

Our tutors are from top schools around the world, and they are waiting for you 24/7, anytime, anywhere.

Homework- One to One Solutions
Understand concepts to solve better
Get your doubts solved instantly

Maths-

General

Easy

Question

$t a n space 40 to the power of ring operator plus t a n space 80 to the power of ring operator minus √ 3 t a n space 40 to the power of ring operator t a n space 80 to the power of ring operator equals$

$\sqrt{3}$
$- \sqrt{3}$
$\frac{1}{\sqrt{3}}$
$\frac{- 1}{\sqrt{3}}$

hint Hint:

In this question we will use the formula of $tan open parentheses A plus B close parentheses space equals space fraction numerator tan open parentheses A close parentheses plus tan open parentheses B close parentheses over denominator 1 minus tan open parentheses A close parentheses tan open parentheses B close parentheses end fraction$ in which we put A = $40 to the power of ring operator$ and B =
$80 to the power of ring operator$ . After rearranging the equation we will get the answer.

The correct answer is: $negative square root of 3$

In this question we are given expression
$t a n space 40 to the power of ring operator plus t a n space 80 to the power of ring operator minus √ 3 t a n space 40 to the power of ring operator t a n space 80 to the power of ring operator$
Step1: Using the formula of $tan open parentheses A plus B close parentheses$
We know that $tan open parentheses A plus B close parentheses space equals space fraction numerator tan open parentheses A close parentheses plus tan open parentheses B close parentheses over denominator 1 minus tan open parentheses A close parentheses tan open parentheses B close parentheses end fraction$
We can also rewrite the above expression as $tan open parentheses A close parentheses plus tan open parentheses B close parentheses space equals space tan open parentheses A plus B close parentheses minus tan open parentheses A plus B close parentheses tan open parentheses A close parentheses tan open parentheses B close parentheses$
Step2: Putting the values of A and B in the above formula
By putting A = $40 to the power of ring operator$ and B = $80 to the power of ring operator$ , we get,
$tan open parentheses 40 to the power of ring operator close parentheses plus tan open parentheses 80 to the power of ring operator close parentheses space equals space tan open parentheses 40 to the power of ring operator plus 80 to the power of ring operator close parentheses space minus space tan open parentheses 40 to the power of ring operator plus 80 to the power of ring operator close parentheses tan open parentheses 40 to the power of ring operator close parentheses tan open parentheses 80 to the power of ring operator close parentheses$
=> $tan open parentheses 40 to the power of ring operator close parentheses plus tan open parentheses 80 to the power of ring operator close parentheses space equals space tan open parentheses 120 to the power of ring operator close parentheses space minus space tan open parentheses 120 to the power of ring operator close parentheses tan open parentheses 40 to the power of ring operator close parentheses tan open parentheses 80 to the power of ring operator close parentheses$
and we know that $tan open parentheses 120 to the power of ring operator close parentheses space equals negative square root of 3$
=> $tan open parentheses 40 to the power of ring operator close parentheses plus tan open parentheses 80 to the power of ring operator close parentheses space equals space minus square root of 3 space minus space left parenthesis negative square root of 3 right parenthesis tan open parentheses 40 to the power of ring operator close parentheses tan open parentheses 80 to the power of ring operator close parentheses$
=> $tan open parentheses 40 to the power of ring operator close parentheses plus tan open parentheses 80 to the power of ring operator close parentheses space equals space minus square root of 3 space plus square root of 3 tan open parentheses 40 to the power of ring operator close parentheses tan open parentheses 80 to the power of ring operator close parentheses$
Step3: By rearranging the equation we get
$tan open parentheses 40 to the power of ring operator close parentheses plus tan open parentheses 80 to the power of ring operator close parentheses space minus square root of 3 tan open parentheses 40 to the power of ring operator close parentheses tan open parentheses 80 to the power of ring operator close parentheses space equals space minus square root of 3 space$
So, the value of the expression is $negative square root of 3$

Related Questions to study

$text If end text 0 less than theta less than pi over 2 text and end text 2 sin invisible function application theta equals square root of 3 cos space 10 to the power of ring operator plus sin space 10 to the power of ring operator text then end text theta equals$

$text If end text 0 less than theta less than pi over 2 text and end text 2 sin invisible function application theta equals square root of 3 cos space 10 to the power of ring operator plus sin space 10 to the power of ring operator text then end text theta equals$

$cos space left parenthesis n plus 1 right parenthesis alpha cos space left parenthesis n minus 1 right parenthesis alpha plus sin space left parenthesis n plus 1 right parenthesis alpha sin space left parenthesis n minus 1 right parenthesis alpha equals$

$cos space left parenthesis n plus 1 right parenthesis alpha cos space left parenthesis n minus 1 right parenthesis alpha plus sin space left parenthesis n plus 1 right parenthesis alpha sin space left parenthesis n minus 1 right parenthesis alpha equals$

$sin space 40 to the power of ring operator 35 cos space 19 to the power of ring operator 25 plus cos space 40 to the power of ring operator 35 to the power of ring operator sin space 19 to the power of ring operator 25 equals$

$sin space 40 to the power of ring operator 35 cos space 19 to the power of ring operator 25 plus cos space 40 to the power of ring operator 35 to the power of ring operator sin space 19 to the power of ring operator 25 equals$

parallel

Assertion A: In a right-angled triangle $s i n squared space A plus s i n squared space B plus s e c squared space C equals 2$ Reason $R colon$ if $alpha comma beta$ are complementary angles then $s i n squared space alpha plus s i n squared space beta equals 1$

Assertion A: In a right-angled triangle $s i n squared space A plus s i n squared space B plus s e c squared space C equals 2$ Reason $R colon$ if $alpha comma beta$ are complementary angles then $s i n squared space alpha plus s i n squared space beta equals 1$

AB is a line segment of length 24 cm and C is its middle point. On AB, A and CB semi-circles are described. The radius of circle which touches all these semi-circles is

AB is a line segment of length 24 cm and C is its middle point. On AB, A and CB semi-circles are described. The radius of circle which touches all these semi-circles is

in a $triangle P Q R$ $3 sin space P plus 4 cos space Q equals 6$ and $4 sin space Q plus 3 cos$ p=1 then

in a $triangle P Q R$ $3 sin space P plus 4 cos space Q equals 6$ and $4 sin space Q plus 3 cos$ p=1 then

parallel

The expression $fraction numerator tan space A over denominator 1 minus cat space A end fraction plus fraction numerator cot space A over denominator 1 minus tan space d end fraction$ can be written as

The expression $fraction numerator tan space A over denominator 1 minus cat space A end fraction plus fraction numerator cot space A over denominator 1 minus tan space d end fraction$ can be written as

if $straight f subscript straight k left parenthesis straight x right parenthesis equals 1 divided by straight k left parenthesis sin to the power of straight k space straight x plus cos to the power of straight k space straight x right parenthesis$ where $straight x element of straight R comma straight k greater or equal than 1$ then $straight f subscript 4 left parenthesis straight x right parenthesis minus straight f subscript 6 left parenthesis straight x right parenthesis equals$

if $straight f subscript straight k left parenthesis straight x right parenthesis equals 1 divided by straight k left parenthesis sin to the power of straight k space straight x plus cos to the power of straight k space straight x right parenthesis$ where $straight x element of straight R comma straight k greater or equal than 1$ then $straight f subscript 4 left parenthesis straight x right parenthesis minus straight f subscript 6 left parenthesis straight x right parenthesis equals$

Two arcs of same length of two different circles subtended angles of $25 to the power of ring operator$ and $75 to the power of ring operator$ at their centers respectively. Then the ratio of the radii of the circles is

Two arcs of same length of two different circles subtended angles of $25 to the power of ring operator$ and $75 to the power of ring operator$ at their centers respectively. Then the ratio of the radii of the circles is

parallel

Let $theta element of left parenthesis 0 comma pi divided by 4 right parenthesis$ and $straight t subscript 1 equals left parenthesis tan space theta right parenthesis to the power of me theta end exponent comma straight t subscript 2 equals left parenthesis tan space theta right parenthesis to the power of cot space theta end exponent comma straight t subscript 3 equals left parenthesis cot space theta right parenthesis to the power of con space theta end exponent straight t subscript 4 equals left parenthesis cot space theta right parenthesis to the power of cos space theta end exponent$ then

Let $theta element of left parenthesis 0 comma pi divided by 4 right parenthesis$ and $straight t subscript 1 equals left parenthesis tan space theta right parenthesis to the power of me theta end exponent comma straight t subscript 2 equals left parenthesis tan space theta right parenthesis to the power of cot space theta end exponent comma straight t subscript 3 equals left parenthesis cot space theta right parenthesis to the power of con space theta end exponent straight t subscript 4 equals left parenthesis cot space theta right parenthesis to the power of cos space theta end exponent$ then

$straight a equals sec space 2 to the power of ring operator comma straight b equals sec space 2 rightwards double arrow$

$straight a equals sec space 2 to the power of ring operator comma straight b equals sec space 2 rightwards double arrow$

I $x equals cos invisible function application 1 to the power of ring operator comma y equals cos invisible function application 1 not stretchy rightwards double arrow$

I $x equals cos invisible function application 1 to the power of ring operator comma y equals cos invisible function application 1 not stretchy rightwards double arrow$

parallel

If ABCD is a cynic quadrilateral such that 12 tan $A minus 5 equals 0$ and 5cos B+3=0, then cos C tan D=

If ABCD is a cynic quadrilateral such that 12 tan $A minus 5 equals 0$ and 5cos B+3=0, then cos C tan D=

$integral fraction numerator d x over denominator square root of x squared plus 2 x plus 1 end root end fraction$ = A log |x + 1| + C for x < – 1 then A is -

$integral fraction numerator d x over denominator square root of x squared plus 2 x plus 1 end root end fraction$ = A log |x + 1| + C for x < – 1 then A is -

$cos space A comma sin space A comma cot space A space$ are in then $tan to the power of 6 straight A minus tan squared space of 1em straight A equals$

$cos space A comma sin space A comma cot space A space$ are in then $tan to the power of 6 straight A minus tan squared space of 1em straight A equals$

parallel

card img

With Turito Academy.

card img

With Turito Foundation.

card img

Get an Expert Advice From Turito.

Turito Academy

card img

With Turito Academy.

Test Prep

card img

With Turito Foundation.