How to use Cofunction Identities to Find the Angle

Question

Using cofunction identies, what steps can one take to find the angle x which makes the statement true?

sec x = csc( 2 x + 45° )

MY ATTEMPTS :

I have tried rearrange sec x = csc( 95° + x), however, I am not sure how to approach the problem.

user id:401635 9k · Accepted Answer

Hint -

$\sec x = \csc(2x + 45°)$

$\csc(90° - x) = \csc(2x + 45°)$

$(90° - x) = (2x + 45°)$

Hope you proceed further.

user id:278967 22k · Accepted Answer

HINT: $$\cos x = \sin (2x+\frac{\pi}{4}) = \cos (\frac{\pi}{2}-2x-\frac{\pi}{4}) = \cos (\frac{\pi}{4}-2x)$$

2 Answers 2