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प्रश्न
Prove that `(sec θ - 1)/(sec θ + 1) = ((sin θ)/(1 + cos θ ))^2`
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उत्तर
LHS = `(sec θ - 1)/(sec θ + 1)`
= `(1/cos θ - 1)/(1/cos θ + 1)`
= `(1 - cos θ)/(1 + cos θ)`
= `(1 - cos θ xx ( 1 + cos θ))/(1 + cos θ xx (1 + cos θ))`
= `(1 - cos^2 θ)/(1 + cos θ)^2`
= `(sin^2 θ)/(1 + cos θ)^2`
= `((sin θ)/(1 + cos θ ))^2`
= RHS
संबंधित प्रश्न
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`(tan A + tan B)/(cot A + cot B) = tan A tan B`
Prove the following identities:
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Prove the following identity :
`(1 + sinA)/(1 - sinA) = (cosecA + 1)/(cosecA - 1)`
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If x = r sin θ cos Φ, y = r sin θ sin Φ and z = r cos θ, prove that x2 + y2 + z2 = r2.
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