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Question
If \[\sin \theta = \frac{1}{3}\] then find the value of 2cot2 θ + 2.
Solution
Given:
`sin θ=1/3`
⇒ `1/ sinθ=3`
⇒` cosec θ=3`
We know that,
`cosec^2θ-cot ^2θ=1`
⇒`(3)^2-cot^2θ=1`
⇒ `cot ^2 θ=9-1`
Therefore,
`2 cot ^2 θ+2=2xx8+2`
=`16+2`
= `18`
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Solution :
L.H.S. = cotθ + tanθ
= `cosθ/sinθ + sinθ/cosθ`
= `(square + square)/(sinθ xx cosθ)`
= `1/(sinθ xx cosθ)` ............... `square`
= `1/sinθ xx 1/square`
= cosecθ × secθ
L.H.S. = R.H.S
∴ cotθ + tanθ = cosecθ × secθ
