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Maths-

General

Easy

Question

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

1
$\frac{\sqrt{3}}{2}$
0
-1

hint Hint:

For solving this question we will use the formula of $sin open parentheses A plus B close parentheses space equals space sin open parentheses A close parentheses cos open parentheses B close parentheses plus cos open parentheses A close parentheses sin open parentheses B close parentheses$ and we know that there are $60 space m i n u t e s$ in $1 to the power of ring operator$ .

The correct answer is: $fraction numerator square root of 3 over denominator 2 end fraction$

In this question we are given
$sin open parentheses 40 to the power of ring operator 35 apostrophe close parentheses cos open parentheses 19 to the power of ring operator 25 apostrophe close parentheses plus cos open parentheses 40 to the power of ring operator 35 apostrophe close parentheses sin open parentheses 19 to the power of ring operator 25 apostrophe close parentheses$
We will use the formula of $sin left parenthesis A plus B right parenthesis$
Step1: Using the formula of $sin open parentheses A plus B close parentheses$
$sin open parentheses A plus B close parentheses space equals space sin open parentheses A close parentheses cos open parentheses B close parentheses plus cos open parentheses A close parentheses sin open parentheses B close parentheses$
Here A = $40 to the power of ring operator 35 apostrophe$ and B = $19 to the power of ring operator 25 apostrophe$ ,
Step2: Putting the values of A and B in the formula of $sin open parentheses A plus B close parentheses$
$sin open parentheses 40 to the power of ring operator 35 apostrophe close parentheses cos open parentheses 19 to the power of ring operator 25 apostrophe close parentheses plus cos open parentheses 40 to the power of ring operator 35 apostrophe close parentheses sin open parentheses 19 to the power of ring operator 25 apostrophe close parentheses$
we get,
$sin open parentheses 40 to the power of ring operator 35 apostrophe plus 19 to the power of ring operator 25 apostrophe close parentheses$
=> $sin open parentheses 59 to the power of ring operator 60 apostrophe close parentheses$
We know that there are $60 space m i n u t e s$ in $1 to the power of ring operator$
So, $60 apostrophe space equals 1 to the power of ring operator$
=> $sin open parentheses 60 to the power of ring operator close parentheses$
and we know that the value of $sin open parentheses 60 to the power of ring operator close parentheses$ is $fraction numerator square root of 3 over denominator 2 end fraction$

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