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प्रश्न
Prove the following identity :
cosecθ(1 + cosθ)(cosecθ - cotθ) = 1
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उत्तर
LHS = cosecθ(1 + cosθ)(cosecθ - cotθ)
= `1/sinθ(1 + cosθ)(1/sinθ - cosθ/sinθ)`
= `((1 + cosθ))/sinθ ((1-cosθ)/sinθ)`
= `(1 - cos^2θ)/sin^2θ = sin^2θ/sin^2θ = 1 = RHS`
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संबंधित प्रश्न
Prove the following trigonometric identities.
`tan theta + 1/tan theta = sec theta cosec theta`
Prove the following identities:
`cosA/(1 + sinA) + tanA = secA`
If x = a sin θ and y = bcos θ , write the value of`(b^2 x^2 + a^2 y^2)`
If x = a sin θ and y = b cos θ, what is the value of b2x2 + a2y2?
The value of \[\sqrt{\frac{1 + \cos \theta}{1 - \cos \theta}}\]
Prove the following identity :
`(cot^2θ(secθ - 1))/((1 + sinθ)) = sec^2θ((1-sinθ)/(1 + secθ))`
Choose the correct alternative:
1 + tan2 θ = ?
Prove that `(tan^2 theta - 1)/(tan^2 theta + 1)` = 1 – 2 cos2θ
Prove that `(sintheta + "cosec" theta)/sin theta` = 2 + cot2θ
Factorize: sin3θ + cos3θ
Hence, prove the following identity:
`(sin^3θ + cos^3θ)/(sin θ + cos θ) + sin θ cos θ = 1`
