How to compute the following trigonometric question \sqrt{2}\sin10(\sec5+\frac{2\cos40}{\sin5}-4\sin35)

Libby Boone

Libby Boone

Answered question

2022-04-21

How to compute the following trigonometric question
2sin10(sec5+2cos40sin54sin35)

Answer & Explanation

Deandre Barron

Deandre Barron

Beginner2022-04-22Added 17 answers

Let the expression to be evaluated be x
Since sin10=2sin5cos5, you get:
22(sin5+2cos40cos54sin35sin5cos5)
=22(sin5+2cos40cos52sin35sin10)
We can write:
2cos40cos5=cos45+cos35
2sin35sin10=cos25cos45
Hence,
x=22(sin5+cos45+cos35+cos45cos25)
=22(2+sin5+cos35cos25)
Since
cos35cos25=2sin30sin5=sin5
The final answer is 4.

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