Prove that-

cos²0° – 2 cot²30° + 3 cosec²90° = 2(sec²45° – tan²60°)

cos0° = 1

∴ cos²0° = 1

cot30° = √3

∴ cot²30° = 3

cosec90° = 1

∴ cosec²90° = 1

sec45° = √2

∴ sec²45° = 2

tan60° = √3

tan²60° = 3

∴ LHS = cos²0° – 2 cot²30° + 3 cosec²90°

= 1 - 2 × 3 + 3 × 1

= 1 - 6 + 3

= 4 - 6

= - 2

RHS = 2(sec²45° – tan²60°)

= 2 × (2 - 3)

= 2 × ( -1)

= - 2

- 2 = - 2

∴ LHS = RHS

∴cos²0° – 2 cot²30° + 3 cosec²90° = 2(sec²45° – tan²60°)

Hence Proved