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Question

Prove the following :
(ix) 1cosec A-cot A- 1sinA = 1Sin A-1cosec A+cot A

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Solution

We can write 1cosec A-cot A-1sin A = 1sin A-1cosec A+cot A as1cosec A-cot A+1cosec A+cot A = 1sin A+1sin A = 2sin A ...(i)So, we can prove the above identity in place of 1cosec A-cot A-1sin A = 1sin A-1cosec A+cot A.Taking LHS of (i), we have:1cosec A-cot A+1cosec A+cot A = cosec A+cot A+cosec A-cot Acosec2A-cot 2A= 2 cosec A= 2sinA = RHS of (i)

Hence, proved.

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