Question

${\displaystyle If\sin \theta =\cos (\theta -45°),where \theta \text{is acute, find the value of}\theta }$ .

Answer 1

𝑊𝑒 ℎ𝑎𝑣𝑒,
Sin 𝜃 = cos(𝜃 − 45°)
⟹ cos(90° − 𝜃) = cos(𝜃 − 45°)
Comparing both sides, we get

 ${\displaystyle 90°-\theta =\theta -45°}$

${\displaystyle \Rightarrow \theta +\theta =90°+a=45°}$

${\displaystyle \Rightarrow 2\theta =135°}$

${\displaystyle \Rightarrow \theta ={\left(\frac{135}{2}\right)}^{°}}$ 

∴ 𝜃 = 67.5°