1.

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

Answer»

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.



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