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प्रश्न
If sin θ + sin2 θ = 1 show that: cos2 θ + cos4 θ = 1
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उत्तर
sin θ + sin2 θ = 1 ......[Given]
∴ sin θ = 1 − sin2 θ
∴ sin θ = cos2 θ ......[∵ 1 − sin2 θ = cos2 θ]
∴ sin2 θ = cos4 θ ......[Squaring both the sides]
∴ 1 − cos2 θ = cos4 θ ......[∵ sin2 θ = 1 − cos2 θ]
∴ 1 = cos2 θ + cos4 θ
∴ cos2 θ + cos4 θ = 1
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संबंधित प्रश्न
If sinθ + sin2 θ = 1, prove that cos2 θ + cos4 θ = 1
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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
