sin(A)+cos(A)=1/4. Find sin(A)cos(A) without a calculator

Rosemary Chase

Rosemary Chase

Answered question

2022-11-07

sin ( A ) + cos ( A ) = 1 / 4. Find sin ( A ) cos ( A ) without a calculator. I think it is about double angles formula sin ( 2 A ) = 2 sin A cos A but I still didn't know how to solve it.

Answer & Explanation

erlentzed

erlentzed

Beginner2022-11-08Added 22 answers

Squaring both sides we have
sin 2 ( A ) + 2 sin ( A ) cos ( A ) + cos 2 ( A ) = 1 16 1 cos 2 ( A ) + 2 sin ( A ) cos ( A ) + cos 2 ( A ) = 1 16 2 sin ( A ) cos ( A ) = 15 16 sin ( A ) cos ( A ) = 15 32
where the only tool we used was that sin 2 x = 1 cos 2 x

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