Question

If A and (2A – 45°) are acute angles such that sin A = cos (2A – 45°), then tan A is equal to

(a) 0
(b) 13√
(c) 1
(d) √3


please answer it fastt

Answer 1

(c) 1

Explanation:

`\sin \: A = \cos(2A - 45 \degree) \\ \\ \cos(90 \degree - A )= \cos(2A - 45 \degree) \\ \\ 90 \degree - A = 2A - 45 \degree \\ \\ 90 \degree - 45 \degree = 2A -A \\ \\ 45 \degree = A \\ \\ A = 45 \degree \\ \\ \tan \: A = \tan \: 45 \degree \\ \\ \huge \red{ \boxed{\tan \: A =1}}`