Advertisements
Advertisements
प्रश्न
Prove the following identity :
`(cot^2θ(secθ - 1))/((1 + sinθ)) = sec^2θ((1-sinθ)/(1 + secθ))`
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 the following trigonometric identities.
`(cot^2 A(sec A - 1))/(1 + sin A) = sec^2 A ((1 - sin A)/(1 + sec A))`
if `a cos^3 theta + 3a cos theta sin^2 theta = m, a sin^3 theta + 3 a cos^2 theta sin theta = n`Prove that `(m + n)^(2/3) + (m - n)^(2/3)`
Prove the following identities:
cosec A(1 + cos A) (cosec A – cot A) = 1
Prove the following identities:
`cosA/(1 - sinA) = sec A + tan A`
Prove the following identities:
(1 + cot A – cosec A)(1 + tan A + sec A) = 2
`sqrt((1+cos theta)/(1-cos theta)) + sqrt((1-cos theta )/(1+ cos theta )) = 2 cosec theta`
The value of sin ( \[{45}^° + \theta) - \cos ( {45}^°- \theta)\] is equal to
Verify that the points A(–2, 2), B(2, 2) and C(2, 7) are the vertices of a right-angled triangle.
Choose the correct alternative:
sin θ = `1/2`, then θ = ?
If sec θ + tan θ = `sqrt(3)`, complete the activity to find the value of sec θ – tan θ
Activity:
`square` = 1 + tan2θ ......[Fundamental trigonometric identity]
`square` – tan2θ = 1
(sec θ + tan θ) . (sec θ – tan θ) = `square`
`sqrt(3)*(sectheta - tan theta)` = 1
(sec θ – tan θ) = `square`
