If cosx + sinx = √(2) cosx, What is the value of (cosx - sinx)²+ (cosx + sinx)²?

If cosx + sinx = √(2) cosx, What is the value of (cosx…

If cosx + sinx = $\sqrt{2}$ cosx, What is the value of (cosx - sinx)²+ (cosx + sinx)²?

Show answer & explanation

Correct answer: A

Explanation

The correct answer is option 1 i.e. 2.

Given that

If cosx + sinx = $\sqrt{2}$ cosx

the value of (cosx - sinx)²+ (cosx + sinx)²

⇒ cos²x + sin²x - 2cosx sinx + cos²x + sin²x + 2cosx sinx

⇒ 2 (cos²x + sin²x)

⇒ 2 × 1 = 2