Question

Prove that cos² 0° – 2 cot² 30° + 3 cosec² 90° = 2(sec² 45° – tan² 60°)

Answer 1

L.H.S. = cos² 0° – 2 cot² 30° + 3 cosec² 90°

= (1)² – 2(√3)² + 3(1)²

= 1 – 2 × 3 + 3

= 1 – 6 + 3 = -2

R.H.S. = 2(sec² 45° – tan² 60°)

= 2[(√2)² – (√3)²]

= 2(2 – 3) = 2 × (-1) = -2

Thus, L.H.S. = R.H.S.