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Question
Show that `sqrt((1-cos A)/(1 + cos A)) = sinA/(1 + cosA)`
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Solution
`L.H.S = sqrt((1-cosA)/(1 + cosA))`
`= sqrt(((1-cosA)(1 + cosA))/((1+ cosA)(1 + cosA)))`
`= sqrt((1 - cos^2A)/(1 + cosA)^2`
`= sqrt((sin^2A)/(1+cosA)^2)`
`= sinA/(1 + cosA)`
= R.H.S
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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
`1/sin^2θ - 1/cos^2θ - 1/tan^2θ - 1/cot^2θ - 1/sec^2θ - 1/("cosec"^2θ) = -3`, then find the value of θ.
Factorize: sin3θ + cos3θ
Hence, prove the following identity:
`(sin^3θ + cos^3θ)/(sin θ + cos θ) + sin θ cos θ = 1`
