Question

Evaluate 2 sec² θ + 3 cosec² θ – 2 sin θ cos θ if θ = 45°.

Answer 1

2 sec² θ + 3 cosec² θ – 2 sin θ cos θ

= `2(sqrt(2))^2 + 3(sqrt(2))^2 - 2. 1/sqrt(2). 1/sqrt(2)`  ...[∵ θ = 45°]

= `2 xx 2 + 3 xx 2 - 2 xx 1/2`

= 4 + 6 – 1

= 9