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प्रश्न
Prove the following trigonometric identities.
`tan theta + 1/tan theta` = sec θ.cosec θ
Prove the following:
`tan theta + 1/tan theta` = sec θ.cosec θ
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उत्तर
We know that `sec^2 theta - tan^2 theta = 1`
So,
`tan theta + 1/tan theta = (tan^2 theta + 1)/tan theta`
`= sec^2 theta/tan theta`
`= sec theta sec theta/tan theta`
`= sec theta = (1/cos theta)/(sin theta/cos theta)`
`= sec theta cosec theta`
संबंधित प्रश्न
Prove that `(sec theta - 1)/(sec theta + 1) = ((sin theta)/(1 + cos theta))^2`
Prove the following identities:
`(sec A - 1)/(sec A + 1) = (1 - cos A)/(1 + cos A)`
Prove the following identities:
`sqrt((1 - cosA)/(1 + cosA)) = sinA/(1 + cosA)`
Prove the following identities:
`(sin theta + 1 - cos theta)/(cos theta - 1 + sin theta) = (1 + sin theta)/(cos theta)`
Prove the following identities:
`(cos theta "cosec" theta - sin theta sec theta )/(cos theta + sin theta) = "cosec" theta - sec theta`
`(tan A + tanB )/(cot A + cot B) = tan A tan B`
Write the value of ` cosec^2 (90°- theta ) - tan^2 theta`
Prove the following identity :
( 1 + cotθ - cosecθ) ( 1 + tanθ + secθ)
Prove the following identity :
`sqrt((1 - cosA)/(1 + cosA)) = sinA/(1 + cosA)`
If 3 sin A + 5 cos A = 5, then show that 5 sin A – 3 cos A = ± 3.
