Question

Prove that √1-sin^2/sin^2=cot

Answer 1

Step-by-step explanation:

root 1-sin square x = cosx

root sin square x = sinx(after cancellation of root and square)

cosx/sinx=cotx

Hence proved

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Answer 2

Step-by-step explanation:

To prove:-

$\sqrt{ \frac{1 - { \sin}^{2} \theta }{ { \sin}^{2} \theta } } = \cot \theta$

Proof:-

$LHS = \sqrt{ \frac{1 - { \sin}^{2} \theta }{ { \sin}^{2} \theta } }$

$\implies \: \frac{ \not \sqrt{ { \cos}^{ \not2} \theta} }{ \not\sqrt{{sin}^{ \not2} \theta} } \: \: \: \: \: \: \: \: \: \: \: \: ( {1 - { \sin}^{ 2} \theta} = { \cos}^{2} \theta)$

$\implies \: \frac{ \cos \theta}{ \sin \theta}$

$\implies \: \cot \theta = RHS$

Since LHS = RHS, hence proved