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Question
If cosec θ = 2x and \[5\left( x^2 - \frac{1}{x^2} \right)\] \[2\left( x^2 - \frac{1}{x^2} \right)\]
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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L.H.S = `square`
= (sin2A + cos2A) `(square)`
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= `square`
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Activity:
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= `square/sintheta + sintheta/costheta`
= `(cos^2theta + sin^2theta)/square`
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Solution:
In Δ ABC, ∠ABC = 90°, ∠C = θ°
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Factorize: sin3θ + cos3θ
Hence, prove the following identity:
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