Q. 205.0( 5 Votes )

Prove that-

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

Answer :

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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