1.

Prove the following :tan x + cot x = 2 cosec 2x

Answer»

L.H.S. = tan x + cot x

\(\frac {sin\,x}{cos\,x} + \frac {cos\,x}{sin\, x}\)

\(\frac {sin^2x+cos^2x}{sin\,x\,cos\,x}\)

\(\frac{1}{sin\,x\,cos\,x}=\frac{2}{2sin\,x\,cos\,x}\)

=\(\frac{1}{sin\,2x}\)

= 2 cosec 2x = R.H.S



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