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प्रश्न
Prove the following identity :
`(1 - sin^2θ)sec^2θ = 1`
उत्तर
`(1 - sin^2θ)sec^2θ = 1`
Consider L.H.S = `cos^2θsec^2θ`
= `cos^2θ xx 1/cos^2θ = 1`
= R.H.S
Hence proved.
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Show that, cotθ + tanθ = cosecθ × secθ
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
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Statement 2: cosec2θ + cot2θ = 1
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