Question

`If sin theta = cos( theta - 45° ),where   theta   " 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

 ` 90° - theta = theta - 45°`

` ⇒ theta + theta = 90° + a=45°`

`⇒ 2 theta = 135°`

`⇒ theta = ((135)/2)^°` 

∴ 𝜃 = 67.5°