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प्रश्न
Prove that (cosec A - sin A)( sec A - cos A) sec2 A = tan A.
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उत्तर
LHS = (cosec A - sin A)(sec A - cos A). sec2A
= `(1/sin A - sin A).(1/cos A - cos A). 1/cos^2 A`
= `(1- sin^2A)/sin A.(1- cos^2 A)/(cos A) xx 1/cos^2 A`
= `cos^2 A/sin A xx sin^2 A/cos A xx 1/cos^2 A ....[ ∵ ( 1 - sin^2 A) = cos^2 A, 1 - cos^2 A = sin^2 A]`
= `sin A/cos A = tan A`
= RHS
Hence proved.
संबंधित प्रश्न
Prove the following trigonometric identities.
`(cos A cosec A - sin A sec A)/(cos A + sin A) = cosec A - sec A`
Prove that `sqrt((1 + cos theta)/(1 - cos theta)) + sqrt((1 - cos theta)/(1 + cos theta)) = 2 cosec theta`
Prove the following identities:
`(sinAtanA)/(1 - cosA) = 1 + secA`
Write the value of `3 cot^2 theta - 3 cosec^2 theta.`
Prove the following identity :
`(cosA + sinA)^2 + (cosA - sinA)^2 = 2`
Evaluate:
`(tan 65°)/(cot 25°)`
Prove that `( 1 + sin θ)/(1 - sin θ) = 1 + 2 tan θ/cos θ + 2 tan^2 θ` .
If a cos θ – b sin θ = c, then prove that (a sin θ + b cos θ) = `± sqrt(a^2 + b^2 - c^2)`
Prove that `(sin^2θ)/(cos θ) + cos θ = sec θ`.
`sqrt((1 - cos^2theta) sec^2 theta) = tan theta`
