Advertisements
Advertisements
प्रश्न
Prove the following identity :
`(cot^2θ(secθ - 1))/((1 + sinθ)) = sec^2θ((1-sinθ)/(1 + secθ))`
Advertisements
उत्तर
LHS = `(cot^2θ(secθ - 1))/((1 + sinθ)) `
= `(cot^2θ(secθ - 1)(1 - sinθ)(secθ + 1))/((1 + sinθ)(1 - sinθ)(secθ + 1))`
= `(cot^2θ(secθ - 1)(secθ + 1)(1 - sinθ))/((1 + sinθ)(1 - sinθ)(secθ + 1))`
= `(cot^2θ(sec^2θ - 1)(1 - sinθ))/((1 - sin^2θ)(1 + secθ))`
= `(cot^2θ(tan^2θ)(1 - sinθ))/((cos^2θ)(1 + secθ))` (∵ `tan^2θ = sec^2θ - 1,1 - sin^2θ = cos^2θ`)
= `((cotθtanθ)^2(1 - sinθ))/((cos^2θ)(1 + secθ))`
= `(1(1 - sinθ))/((cos^2θ)(1 + secθ))` (∵ cotθtanθ = 1)
= `sec^2θ((1 - sinθ)/(1 + secθ))`
APPEARS IN
संबंधित प्रश्न
Prove that ` \frac{\sin \theta -\cos \theta +1}{\sin\theta +\cos \theta -1}=\frac{1}{\sec \theta -\tan \theta }` using the identity sec2 θ = 1 + tan2 θ.
Prove the following trigonometric identities.
`"cosec" theta sqrt(1 - cos^2 theta) = 1`
Prove the following trigonometric identities.
`sqrt((1 - cos theta)/(1 + cos theta)) = cosec theta - cot theta`
Prove the following identities:
`sqrt((1 - sinA)/(1 + sinA)) = cosA/(1 + sinA)`
Prove the following identities:
`cosA/(1 + sinA) + tanA = secA`
`(cos ec^theta + cot theta )/( cos ec theta - cot theta ) = (cosec theta + cot theta )^2 = 1+2 cot^2 theta + 2cosec theta cot theta`
If sec2 θ (1 + sin θ) (1 − sin θ) = k, then find the value of k.
Prove the following identity :
`(1 - sin^2θ)sec^2θ = 1`
Prove that `[(1 + sin theta - cos theta)/(1 + sin theta + cos theta)]^2 = (1 - cos theta)/(1 + cos theta)`
Prove that sin2A . tan A + cos2A . cot A + 2 sin A . cos A = tan A + cot A.
