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प्रश्न
Prove that:
(tan A + cot A) (cosec A – sin A) (sec A – cos A) = 1
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उत्तर
(tan A + cot A) (cosec A – sin A) (sec A – cos A)
= `(sinA/cosA + cosA/sinA)(1/sinA - sinA)(1/cosA - cosA)`
= `((sin^2A + cos^2A)/(sinAcosA))((1 - sin^2A)/sinA)((1 - cos^2A)/cosA)`
= `(1/(sinAcosA))(cos^2A/sinA)(sin^2A/cosA)`
= 1
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संबंधित प्रश्न
Prove the following trigonometric identities.
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Prove the following identities:
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Prove the following identities:
`(cosecA)/(cosecA - 1) + (cosecA)/(cosecA + 1) = 2sec^2A`
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`sqrt((1 - cosA)/(1 + cosA)) = sinA/(1 + cosA)`
Prove the following identity :
`(sec^2θ - sin^2θ)/tan^2θ = cosec^2θ - cos^2θ`
Prove that sec2θ – cos2θ = tan2θ + sin2θ.
If cot θ = `40/9`, find the values of cosec θ and sinθ,
We have, 1 + cot2θ = cosec2θ
1 + `square` = cosec2θ
1 + `square` = cosec2θ
`(square + square)/square` = cosec2θ
`square/square` = cosec2θ ......[Taking root on the both side]
cosec θ = `41/9`
and sin θ = `1/("cosec" θ)`
sin θ = `1/square`
∴ sin θ = `9/41`
The value is cosec θ = `41/9`, and sin θ = `9/41`
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