Question

if sin theta + cod theta = root 2 cos theta, show that cot theta =root 2+1

Answer 1

The answer is given below :

Given,

sinθ + cosθ = √2 cosθ

=> 1/√2 sinθ + 1/√2 cosθ = cosθ

=> sin45 sinθ + cos45 cosθ = cosθ, sin

=> cos (45 - θ) = cosθ

=> 45 - θ = θ

=> 2θ = 45

=> θ = 45/2

Now,

cotθ

= cot (45/2)

= √2 + 1 [Proved]

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