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Question
Prove the following:
2cosec 2x + cosec x = `secx cot(x/2)`
Solution
L.H.S. = 2cosec 2x + cosec x
= `2/(sin2x) + 1/sinx`
= `2/(2sin x cosx) + 1/sinx`
= `1/(sinx cosx) + 1/sinx`
= `(1 + cosx)/(sinx cosx)`
= `(2cos^2(x/2))/([2sin(x/2)cos(x/2)]cosx`
= `1/cosx * (cos(x/2))/(sin(x/2)`
= `sec x cot (x/2)`
= R.H.S.
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