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Question
If cosec θ = 2x and \[5\left( x^2 - \frac{1}{x^2} \right)\] \[2\left( x^2 - \frac{1}{x^2} \right)\]
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Solution
Given:
`cosecθ=2x, cot θ2/x`
We know that,
`cosec^2 θ-cot^2 θ=1`
⇒` (2x)^2-(2/x)^2=1`
⇒` 4x^2-4/x^2=1`
⇒ `4(x^2-1/x^2)=1`
⇒`2xx2xx(x^2-1/x^2)=1`
⇒ `2(x^2-1/x^2)=1/2`
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Solution :
L.H.S. = cotθ + tanθ
= `cosθ/sinθ + sinθ/cosθ`
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= `1/(sinθ xx cosθ)` ............... `square`
= `1/sinθ xx 1/square`
= cosecθ × secθ
L.H.S. = R.H.S
∴ cotθ + tanθ = cosecθ × secθ
