Question

Prove that 4 cot² 45° – sec² 60° – sin² 30° = – 1/4

Answer 1

4 cot² 45° – sec² 60° – sin² 30° = – 1/4

L.H.S. = 4 cot² 45° – sec² 60° – sin² 30°

= 4(1)² – (2)² – \({ \left( \frac { 1 }{ 2 } \right) }^{ 2 }\)

= 4 – 4 – 1/4 = –1/4

= R.H.S.

Hence, L.H.S. = R.H.S.