Can someone explain why I get wrong answer in simplifying this expression? sin &#x2061;<!--

Justine Webster

Justine Webster

Answered question

2022-04-12

Can someone explain why I get wrong answer in simplifying this expression?
sin 11 π 12 sin 29 π 12 cos 13 π 12 cos 41 π 12
If we rewrite the expression with new angles,
29 π 12 5 π 12 and 13 π 12 11 π 12
we don't change the value of the expression. But, if we now use sine of sum of angles, we get 1 2 instead of 0.
Why does this happen? Do angles need to be in the same quadrant for the formula to work?

Answer & Explanation

notemilyu1208

notemilyu1208

Beginner2022-04-13Added 20 answers

No, you don't get 1 2 . You get 0 too, because
sin ( 11 π 12 ) sin ( 5 π 12 ) cos ( 11 π 12 ) cos ( 41 π 12 ) = sin ( 11 π 12 ) sin ( 5 π 12 ) cos ( 11 π 12 ) cos ( 3 π + 5 π 12 ) = sin ( 11 π 12 ) sin ( 5 π 12 ) + cos ( 11 π 12 ) cos ( 5 π 12 ) = cos ( 11 π 12 5 π 12 ) = cos ( π 2 ) = 0.

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