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

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

Answer»

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.

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