If sin ⁡ ( x ) a = cos ⁡ ( x ) b then...

logiski9s

logiski9s

Answered

2022-07-09

If sin ( x ) a = cos ( x ) b then a sin ( 2 x ) + b cos ( 2 x ) = ?
b sin ( x ) = a cos ( x )
tan ( x ) = a b
I couldn't simplify after that.

Answer & Explanation

Dayana Zuniga

Dayana Zuniga

Expert

2022-07-10Added 16 answers

Though there are lots of answers here, I'd like to put an answer with almost no computations.
a sin ( 2 x ) + b cos ( 2 x ) = a sin ( x ) ( sin ( x ) sin ( 2 x ) + cos ( x ) cos ( 2 x ) ) = a sin ( x ) cos ( x ) = b
Sylvia Byrd

Sylvia Byrd

Expert

2022-07-11Added 6 answers

tan x = a b and from here
a sin 2 x + b cos 2 x = 2 a 2 b 1 + a 2 b 2 + b a 2 b 1 + a 2 b 2 = b

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