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प्रश्न
Prove the following identity :
`cos^4A - sin^4A = 2cos^2A - 1`
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उत्तर
LHS = `cos^4A - sin^4A`
= `(cos^2A - sin^2A)(cos^2A + sin^2A)`
= `{cos^2A - (1 - cos^2A)} = 2cos^2A - 1` = RHS
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संबंधित प्रश्न
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What is the value of \[\frac{\tan^2 \theta - \sec^2 \theta}{\cot^2 \theta - {cosec}^2 \theta}\]
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Prove that ( 1 + tan A)2 + (1 - tan A)2 = 2 sec2A
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Sec A( 1 + sin A)( sec A - tan A) = 1.
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
