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

In $triangle A B C comma left parenthesis a plus b plus c right parenthesis left parenthesis tan invisible function application A divided by 2 plus tan invisible function application B divided by 2 right parenthesis tan invisible function application C divided by 2 equals$

c
$c / 2$
2c
3c

The correct answer is: 2c

In this question we have to find the value of $fraction numerator left parenthesis a plus b plus c right parenthesis left parenthesis tan open parentheses begin display style A over 2 end style close parentheses plus tan open parentheses begin display style B over 2 end style close parentheses right parenthesis over denominator tan open parentheses begin display style C over 2 end style close parentheses end fraction$
Step1: By using formula from Solution of triangle
We know that
$tan open parentheses A over 2 close parentheses equals square root of fraction numerator left parenthesis s minus b right parenthesis left parenthesis s minus c right parenthesis over denominator s left parenthesis s minus a right parenthesis end fraction end root tan open parentheses B over 2 close parentheses equals square root of fraction numerator left parenthesis s minus a right parenthesis left parenthesis s minus c right parenthesis over denominator s left parenthesis s minus b right parenthesis end fraction end root tan open parentheses C over 2 close parentheses equals square root of fraction numerator left parenthesis s minus a right parenthesis left parenthesis s minus b right parenthesis over denominator s left parenthesis s minus c right parenthesis end fraction end root$
by putting these values in the given expression we get,
=> $fraction numerator left parenthesis a plus b plus c right parenthesis left parenthesis square root of fraction numerator left parenthesis s minus b right parenthesis left parenthesis s minus c right parenthesis over denominator s left parenthesis s minus a right parenthesis end fraction end root plus square root of fraction numerator left parenthesis s minus a right parenthesis left parenthesis s minus c right parenthesis over denominator s left parenthesis s minus b right parenthesis end fraction end root right parenthesis over denominator square root of fraction numerator left parenthesis s minus a right parenthesis left parenthesis s minus b right parenthesis over denominator s left parenthesis s minus c right parenthesis end fraction end root end fraction$
$fraction numerator left parenthesis a plus b plus c right parenthesis square root of begin display style fraction numerator left parenthesis s minus c right parenthesis over denominator s end fraction end style end root left parenthesis square root of fraction numerator left parenthesis s minus b right parenthesis over denominator left parenthesis s minus a right parenthesis end fraction end root plus square root of fraction numerator left parenthesis s minus a right parenthesis over denominator left parenthesis s minus b right parenthesis end fraction end root right parenthesis over denominator square root of begin display style fraction numerator 1 over denominator s left parenthesis s minus c right parenthesis end fraction end style end root square root of fraction numerator left parenthesis s minus a right parenthesis left parenthesis s minus b right parenthesis over denominator 1 end fraction end root end fraction$
$fraction numerator left parenthesis a plus b plus c right parenthesis left parenthesis s minus c right parenthesis left parenthesis square root of fraction numerator left parenthesis s minus b right parenthesis over denominator left parenthesis s minus a right parenthesis end fraction end root plus square root of fraction numerator left parenthesis s minus a right parenthesis over denominator left parenthesis s minus b right parenthesis end fraction end root right parenthesis over denominator square root of left parenthesis s minus a right parenthesis left parenthesis s minus b right parenthesis end root end fraction$
$fraction numerator left parenthesis a plus b plus c right parenthesis left parenthesis s minus c right parenthesis left parenthesis begin display style fraction numerator left parenthesis s minus b right parenthesis plus left parenthesis s minus a right parenthesis over denominator square root of left parenthesis s minus a right parenthesis left parenthesis s minus b right parenthesis end root end fraction end style right parenthesis over denominator square root of left parenthesis s minus a right parenthesis left parenthesis s minus b right parenthesis end root end fraction$
$fraction numerator left parenthesis a plus b plus c right parenthesis left parenthesis s minus c right parenthesis left parenthesis left parenthesis s minus b right parenthesis plus left parenthesis s minus a right parenthesis right parenthesis over denominator left parenthesis s minus a right parenthesis left parenthesis s minus b right parenthesis end fraction$
We know that $a plus b plus c equals space 2 s$
$fraction numerator left parenthesis 2 s right parenthesis left parenthesis s minus c right parenthesis left parenthesis left parenthesis 2 s minus b minus a right parenthesis right parenthesis over denominator left parenthesis s minus a right parenthesis left parenthesis s minus b right parenthesis end fraction$

Related Questions to study

If the angles of the Δ are in A.P then $3 R squared equals 1$

If the angles of the Δ are in A.P then $3 R squared equals 1$

In $capital delta A B C comma c left parenthesis a cos invisible function application B minus b cos invisible function application A right parenthesis equals$

In $capital delta A B C comma c left parenthesis a cos invisible function application B minus b cos invisible function application A right parenthesis equals$

In $triangle A B C comma sum left parenthesis a squared s i n invisible function application left parenthesis B minus C right parenthesis right parenthesis divided by left parenthesis s i n invisible function application A right parenthesis equals$

In $triangle A B C comma sum left parenthesis a squared s i n invisible function application left parenthesis B minus C right parenthesis right parenthesis divided by left parenthesis s i n invisible function application A right parenthesis equals$

parallel

In $capital delta A B C comma sum a cubed s i n invisible function application left parenthesis B minus C right parenthesis equals$

In $capital delta A B C comma sum a cubed s i n invisible function application left parenthesis B minus C right parenthesis equals$

When CO₂ dissolves in water the following equilibrium is established, CO₂+2H₂O $rightwards harpoon over leftwards harpoon$ H₃O++HCO₃^– for which the equilibrium constant 3.8 $rightwards harpoon over leftwards harpoon$ 10^–7 and pH = 6.0. The ratio of $open square brackets H C O subscript 3 end subscript close square brackets open square brackets H C O subscript 3 end subscript superscript minus end superscript close square brackets t o blank open square brackets C O subscript 2 end subscript close square brackets$ would be

When CO₂ dissolves in water the following equilibrium is established, CO₂+2H₂O $rightwards harpoon over leftwards harpoon$ H₃O++HCO₃^– for which the equilibrium constant 3.8 $rightwards harpoon over leftwards harpoon$ 10^–7 and pH = 6.0. The ratio of $open square brackets H C O subscript 3 end subscript close square brackets open square brackets H C O subscript 3 end subscript superscript minus end superscript close square brackets t o blank open square brackets C O subscript 2 end subscript close square brackets$ would be

Chemistry-General

In $triangle A B C comma a b c sin invisible function application A divided by 2 space sin invisible function application B divided by 2 space sin invisible function application C divided by 2 equals$

In $triangle A B C comma a b c sin invisible function application A divided by 2 space sin invisible function application B divided by 2 space sin invisible function application C divided by 2 equals$

parallel

In $capital delta A B C comma a squared c o t invisible function application A plus b squared c o t invisible function application B plus C squared c o t invisible function application C equals$

In $capital delta A B C comma a squared c o t invisible function application A plus b squared c o t invisible function application B plus C squared c o t invisible function application C equals$

In $triangle A B C comma c o t invisible function application A divided by 2 plus c o t invisible function application B divided by 2 plus c o t invisible function application C divided by 2 equals$

In $triangle A B C comma c o t invisible function application A divided by 2 plus c o t invisible function application B divided by 2 plus c o t invisible function application C divided by 2 equals$

In $capital delta A B C comma c o t invisible function application A plus c o t invisible function application B plus c o t invisible function application C equals$

In $capital delta A B C comma c o t invisible function application A plus c o t invisible function application B plus c o t invisible function application C equals$

parallel

In $triangle A B C comma 4 R capital delta sin invisible function application A divided by 2 space sin invisible function application B divided by 2 space sin invisible function application C divided by 2 equals$

In $triangle A B C comma 4 R capital delta sin invisible function application A divided by 2 space sin invisible function application B divided by 2 space sin invisible function application C divided by 2 equals$

If 'O' is the Orthocentre of $triangle A B C$ then $O A equals$

If 'O' is the Orthocentre of $triangle A B C$ then $O A equals$

In $I n triangle A B C comma sum a cubed c o s invisible function application left parenthesis B minus C right parenthesis equals$

In $I n triangle A B C comma sum a cubed c o s invisible function application left parenthesis B minus C right parenthesis equals$

parallel

In $triangle A B C comma left parenthesis a plus b right parenthesis cos invisible function application C plus left parenthesis b plus c right parenthesis cos invisible function application A plus left parenthesis c plus a right parenthesis cos invisible function application B equals$

In $triangle A B C comma left parenthesis a plus b right parenthesis cos invisible function application C plus left parenthesis b plus c right parenthesis cos invisible function application A plus left parenthesis c plus a right parenthesis cos invisible function application B equals$

In $triangle A B C comma sum 1 divided by a c o s squared invisible function application A divided by 2 equals$

In $triangle A B C comma sum 1 divided by a c o s squared invisible function application A divided by 2 equals$

In $triangle A B C comma s squared t a n invisible function application A divided by 2 t a n invisible function application B divided by 2 t a n invisible function application C divided by 2 equals$

In $triangle A B C comma s squared t a n invisible function application A divided by 2 t a n invisible function application B divided by 2 t a n invisible function application C divided by 2 equals$

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.