Question

If θ is an acute angle and sinθ = cosθ, find the value of
2 sin²θ – 3 cos²θ + (1/2)tan²θ

Answer 1

Ans. The value of the equation is 0.

The angle θ is acute ( meaning θ is less than 90° and greater than 0° )

Given, sinθ = cosθ

This is possible only for θ = 45°, for 0 <θ <90° (given that θ is acute)

At θ = 45° , cos θ = sinθ = 1/√2 and tanθ = 1

Now using the value θ= 45° in the equation and putting the value of cosθ , sinθ and tanθ.

2sin²θ – 3cos²θ + (1/2)tan²θ

=> 2/2 - 3 × 1/2 + 1/2 × 1

=> 3/2- 3/2

=> 0