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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
If tanθ + sinθ = m and tanθ – sinθ = n, show that `m^2 – n^2 = 4\sqrt{mn}.`
Prove the following trigonometric identities.
`(1 + cos A)/sin A = sin A/(1 - cos A)`
Prove the following trigonometric identities.
`(cos theta - sin theta + 1)/(cos theta + sin theta - 1) = cosec theta + cot theta`
Prove the following identities:
`cot^2A((secA - 1)/(1 + sinA)) + sec^2A((sinA - 1)/(1 + secA)) = 0`
Prove that:
cos A (1 + cot A) + sin A (1 + tan A) = sec A + cosec A
Write the value of `sin theta cos ( 90° - theta )+ cos theta sin ( 90° - theta )`.
Prove the following identities:
`1/(sin θ + cos θ) + 1/(sin θ - cos θ) = (2sin θ)/(1 - 2 cos^2 θ)`.
Prove that cos2θ . (1 + tan2θ) = 1. Complete the activity given below.
Activity:
L.H.S. = `square`
= `cos^2θ xx square` ...`[1 + tan^2θ = square]`
= `(cos θ xx square)^2`
= 12
= 1
= R.H.S.
If tan θ = 3, then `(4 sin theta - cos theta)/(4 sin theta + cos theta)` is equal to ______.
Prove the following:
(sin α + cos α)(tan α + cot α) = sec α + cosec α
