Solve : 2sin^2x + 2cos^2x = 2√2

Question

Solve : ₂sin²x + ₂cos²x = 2\(\sqrt2\)

Answer 1

Given,

⇒ ₂sin²x + ₂cos²x = \(2^{\frac{1}2}+2^{\frac{1}2}\)

On comparing both sides, we have 

sin² x = cos² x = 1/2

Note: If we want to give solution using above two equations then task will become tedious as sin x can be positive at that time cos will be negative and similar 4-5 cases will arise. So inspite of combining all solutions at the end,we proceed as follows

combining both we can say that, 

all the solutions of first 2 equations combined will satisy this single equation 

tan² x = 1