Question

ans this question fast plz ...​

Answer 1

Hey!

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cos ϴ + sin ϴ = √2 cos ϴ


Squaring both sides


(cos ϴ + sin ϴ)² = ( √2 cos ϴ)²

cos²ϴ + 2 cosϴ sinϴ + sin²ϴ = 2 cos²ϴ

cos²ϴ - 2 cos²ϴ + 2 cos ϴ sin ϴ = - sin²ϴ

- ( cos²ϴ - 2 cos ϴ sin ϴ) = - sin²ϴ

cos²ϴ - 2 cos ϴ sin ϴ) = sin²ϴ

cos²ϴ - sin²ϴ = 2 cos ϴ sin ϴ

Using the identity of a² - b²

( cos ϴ + sin ϴ) (cos ϴ - sin ϴ) = 2 cos ϴ sin ϴ

Given, cosϴ - sinϴ = √2 cos ϴ

2 sinϴ cos ϴ = (√2 cos ϴ) (cos ϴ - sin ϴ)

2 sinϴ cosϴ / √2 cosϴ = cos ϴ - sin ϴ

By rationalising, We get,

√2 sin ϴ = cos ϴ - sin ϴ

Hence,Proved.
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Hope it helps!

Answer 2

Here's answer to your question........