1.

If sinθ = cos(θ – 45°), where θ is acute, find the value of θ.

Answer»

We have,

sinθ = cos(θ – 45°), 

Where θ is acute angle.

⇒ cos(90° − θ) = cos(θ − 45°) 

(∵ cos(90° − θ) = sinθ) 

⇒ 90° − θ = θ − 45° 

⇒ 2θ = 90° + 45° = 135°

⇒ θ = \(\frac{135°}{2}\) = 62.5°.

Hence,

The value of θ is 62.5°.



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