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Question
Write the value of \[\cot^2 \theta - \frac{1}{\sin^2 \theta}\]
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Solution
We have,
`cot ^2 -1/ sin^2 θ= cot ^2 θ-(1/ sinθ)^2`
= `cot ^2 θ-(cosec θ)^2`
= `cot^2 θ-cosec^2 θ`
We know that, `cot^2 θ-cosec^2 θ`
Therefore,
\[\cot^2 \theta - \frac{1}{\sin^2 \theta} = - 1\]
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If cot θ = `40/9`, find the values of cosec θ and sinθ,
We have, 1 + cot2θ = cosec2θ
1 + `square` = cosec2θ
1 + `square` = cosec2θ
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and sin θ = `1/("cosec" θ)`
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The value is cosec θ = `41/9`, and sin θ = `9/41`
