Question

sintheta+costheta=underroot costheta
find the value of theta
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Answer 1

Answer:

--> cos θ + sin θ = √2 cos θ

--> sin θ = √2 cos θ - cos θ

=> sin θ = ( √2 - 1 ) cos θ

=> [ sin θ / ( √2 - 1 ) ] = cos θ

=> [ sin θ ( √2 + 1 ) / ( 2 - 1 ) ] = cos θ

0_0 --> We rationalized the denominator in the 2nd step ^_^ 

=> [ √2 sin θ + sin θ ] = cos θ

=> cos θ - sin θ = √2 sin θ

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Answer 2

ANSWER :-

Sin θ+ cos θ = √ cos θ.

By squaring both sides , we get :

( sin θ + cosθ )² = cos θ

=> sin² θ + cos² θ + 2 sinθ. cos θ= cosθ

=> 2 sinθ . cosθ = cosθ

[ .·. sin²θ + cos²θ = 1 ]

=> sin θ = 1/2.

=> θ = 30°