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प्रश्न
Prove that the following identities:
Sec A( 1 + sin A)( sec A - tan A) = 1.
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उत्तर
LHS = sec A(1 + sin A )( sec A - tan A)
= `1/cos A (1 + sin A) (1/cos A - sin A/cos A)`
= `1/cos A (1 + sin A) ((1 - sin A)/cos A)`
= `(1 - sin^2 A)/(cos^2 A) = (cos^2 A)/(cos^2 A)`
= 1
= RHS
Hence proved.
संबंधित प्रश्न
Prove the following trigonometric identity:
`sqrt((1 + sin A)/(1 - sin A)) = sec A + tan A`
Prove the following trigonometric identities.
`(cot A - cos A)/(cot A + cos A) = (cosec A - 1)/(cosec A + 1)`
`sec theta (1- sin theta )( sec theta + tan theta )=1`
`(tan theta)/((sec theta -1))+(tan theta)/((sec theta +1)) = 2 sec theta`
Write the value of `(1 + cot^2 theta ) sin^2 theta`.
What is the value of (1 + cot2 θ) sin2 θ?
If `tan θ = 7/24`, then to find value of cos θ complete the activity given below.
Activity:
sec2θ = 1 + `square` ...[Fundamental tri. identity]
sec2θ = 1 + `square^2`
sec2θ = 1 + `square/576`
sec2θ = `square/576`
sec θ = `square`
cos θ = `square` ...`[cos theta = 1/sectheta]`
Complete the following activity to prove:
cotθ + tanθ = cosecθ × secθ
Activity: L.H.S. = cotθ + tanθ
= `cosθ/sinθ + square/cosθ`
= `(square + sin^2theta)/(sinθ xx cosθ)`
= `1/(sinθ xx cosθ)` ....... ∵ `square`
= `1/sinθ xx 1/cosθ`
= `square xx secθ`
∴ L.H.S. = R.H.S.
If 5 tan β = 4, then `(5 sin β - 2 cos β)/(5 sin β + 2 cos β)` = ______.
(1 – cos2 A) is equal to ______.
