If sin θ = cos θ, 0 ≤ θ ≤ 90° then θ = ?
Question:

If sin θ = cos θ, 0 ≤ θ ≤ 90° then θ = ?
(a) 30°
(b) 45°
(c) 60°
(d) 90°

 

Solution:

Given : $\sin \theta=\cos \theta$

$\Rightarrow \sin \theta=\sin \left(90^{\circ}-\theta\right) \quad\left(\because \sin \left(90^{\circ}-\theta\right)=\cos \theta\right)$

$\Rightarrow \theta=90^{\circ}-\theta$

$\Rightarrow 2 \theta=90^{\circ}$

$\Rightarrow \theta=45^{\circ}$

Hence, the correct option is (b).

 

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