Question

if cos theta + sin theta = √2 cos theta then show that cos theta –sin theta=√2 Sin Theta

Answer 1

Answer:

Step-by-step explanation:

cosθ + sinθ = √2 cosθ

on squaring both sides

cos²θ + sin²θ + 2sinθcosθ = 2cos²θ

sin²θ = 2cos²θ - cos²θ - 2sinθcosθ

on adding sin²θ on both sides

sin²θ + sin²θ = cos²θ -2sinθcosθ + sin²θ

( (a-b)² = a² + b² - 2ab)

2sin²θ =  (cosθ - sinθ)²

√2 sinθ = cosθ - sinθ

Hence, proved

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