Q. 205.0( 5 Votes )

# 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

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