Prove that: cot2θ cosec 2θ−cos2θ =sec2θ−sin2θ

LHS=cot2θcosec2θ−cos2θ=cot2θcosec2θ−cot2θcos2θ=sin2θcos2θsin2θ1−sin2θcos2θcos2θ=sec2θ−sin2θ=RHSHence Proved

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Prove that: { { cosec }^{ 2 } - ^{ 2 }{ } }{ ^{ 2 }{ }

Question

Prove that: $\frac{cosec ^{2} θ - cos ^{2} θ}{cot ^{2} θ} = sec^{2} θ - sin^{2} θ$

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Prove that:

\frac{cosec ^{2} θ - cos ^{2} θ}{cot ^{2} θ} = sec^{2} θ - sin^{2} θ

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L H S = \frac{cosec ^{2} θ - cos ^{2} θ}{cot ^{2} θ}

= \frac{cosec ^{2} θ}{cot ^{2} θ} - \frac{cos ^{2} θ}{cot ^{2} θ}

= \frac{\frac{1}{sin ^{2} θ}}{\frac{cos ^{2} θ}{sin ^{2} θ}} - \frac{cos ^{2} θ}{\frac{cos ^{2} θ}{sin ^{2} θ}}

= sec^{2} θ - sin^{2} θ

= R H S

Hence Proved

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Question Text	Prove that: $\frac{cosec ^{2} θ - cos ^{2} θ}{cot ^{2} θ} = sec^{2} θ - sin^{2} θ$
Answer Type	Text solution:1
Upvotes	150