Question

Given that sin(90 -5ϴ) = Cos(180 - ϴ), Find the value of ϴ​

Answer 1

30°

Explanation:

`\because \: \sin(90 \degree - \theta) = \cos \theta \\ \therefore \: \sin(90 \degree - 5 \theta) = \cos 5\theta....(1) \\ \\ \sin(90 \degree - 5 \theta) = \cos(180 \degree - \theta)...(2) \\ from \: (1) \: and \: (2) \\ \cos 5\theta = \cos(180 \degree - \theta) \\ 5 \theta = 180 \degree - \theta \\ 5 \theta + \theta= 180 \degree \\ 6\theta= 180 \degree \\ \theta = (180 \degree)/(6) \\ \\ \huge \red{ \boxed{\theta = 30 \degree}}`