Question

Prove the identity.
(1-sin^{2}x)csc x=cos x cot x
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Answer 1

Answer:

$(1 - {sin}^{2} x) = \cos ^{2} (x)$

$= \cos^{2} (x) \times \csc(x)$

$= \csc(x) \: = 1 \div \sin(x)$

$= \cos(x) \times( \cos(x) \div \sin(x) )$

$= > \cos(x) \div \sin(x) = \cot(x)$

$= \cos(x ) \times \cot(x)$

hence proved