Advertisements
Advertisements
प्रश्न
Prove the following trigonometric identities.
`sin theta/(1 - cos theta) = cosec theta + cot theta`
Advertisements
उत्तर
We have to prove `sin theta/(1 - cos theta) = cosec theta + cot theta`
We know that `sin^2 theta = cos^2 theta = 1`
`sin theta/(1 - cos theta) = (sin theta (1 + cos theta))/(1 - cos^2 theta)`
`= (sin theta (1 + cos theta))/(1 - cos^2 theta)``
`= (sin theta (1 + cos theta))/(sin^2 theta)`
`= (1 + cos theta)/sin theta`
`= 1/sin theta + cos theta/sin theta`
`= cosec theta + cot theta`
APPEARS IN
संबंधित प्रश्न
Prove the following trigonometric identities.
`(tan^3 theta)/(1 + tan^2 theta) + (cot^3 theta)/(1 + cot^2 theta) = sec theta cosec theta - 2 sin theta cos theta`
Prove the following identities:
`(1 + sin A)/(1 - sin A) = (cosec A + 1)/(cosec A - 1)`
Prove the following identities:
cosec A(1 + cos A) (cosec A – cot A) = 1
Prove the following identities:
`sqrt((1 + sinA)/(1 - sinA)) = cosA/(1 - sinA)`
If sin A + cos A = p and sec A + cosec A = q, then prove that : q(p2 – 1) = 2p.
If 4 cos2 A – 3 = 0, show that: cos 3 A = 4 cos3 A – 3 cos A
`sin theta (1+ tan theta) + cos theta (1+ cot theta) = ( sectheta+ cosec theta)`
Prove that secθ + tanθ =`(costheta)/(1-sintheta)`.
(sec A + tan A) (1 − sin A) = ______.
Prove the following identity :
`(tanθ + secθ - 1)/(tanθ - secθ + 1) = (1 + sinθ)/(cosθ)`
Prove the following identity :
`(cotA + tanB)/(cotB + tanA) = cotAtanB`
Prove the following identity :
`(secθ - tanθ)^2 = (1 - sinθ)/(1 + sinθ)`
Prove the following identity :
`(sec^2θ - sin^2θ)/tan^2θ = cosec^2θ - cos^2θ`
Verify that the points A(–2, 2), B(2, 2) and C(2, 7) are the vertices of a right-angled triangle.
Prove that (sin θ + cosec θ)2 + (cos θ + sec θ)2 = 7 + tan2 θ + cot2 θ.
Prove that `sqrt(2 + tan^2 θ + cot^2 θ) = tan θ + cot θ`.
Prove that sin θ sin( 90° - θ) - cos θ cos( 90° - θ) = 0
If `cos theta/(1 + sin theta) = 1/"a"`, then prove that `("a"^2 - 1)/("a"^2 + 1)` = sin θ
Prove that
sin2A . tan A + cos2A . cot A + 2 sin A . cos A = tan A + cot A
If cos 9α = sinα and 9α < 90°, then the value of tan5α is ______.
