Question

If sin θ = cos θ, where θ is an acute angle, find θ and the value of sec^2 θ + cosec^2 θ.

Solution

1. Divide both sides of sin θ = cos θ by cos θ: tan θ = 1.
2. For an acute angle, tan θ = 1 means θ = 45°.
3. sec 45° = √2 and cosec 45° = √2, so sec^2 45° + cosec^2 45° = 2 + 2 = 4.
4. Therefore, θ = 45° and the value is 4.