Advertisements
Advertisements
प्रश्न
Prove that `(sec theta - 1)/(sec theta + 1) = ((sin theta)/(1 + cos theta))^2`
Advertisements
उत्तर
`(sec theta - 1)/(sec theta + 1)`
`= (1/cos theta - 1)/(1/cos theta + 1)`
= `((1 - cos theta)/cos theta)/((1 + cos theta)/cos theta)`
`= (1 - cos theta)/(1 +cos theta)`
`= (1 - cos theta)/(1 + cos theta) xx (1 + cos theta)/(1+ cos theta)`
`= (1 - cos^2 theta)/(1 + cos theta)^2`
`= sin^2 theta/(1 + cos theta)^2`
`= [sin theta/(1 + cos theta)]^2`
=RHS
Hence proved.
APPEARS IN
संबंधित प्रश्न
(1 + tan θ + sec θ) (1 + cot θ − cosec θ) = ______.
Prove that `(sin theta)/(1-cottheta) + (cos theta)/(1 - tan theta) = cos theta + sin theta`
Prove the following trigonometric identities.
`tan theta + 1/tan theta` = sec θ.cosec θ
Prove the following trigonometric identities.
`(1 - sin θ)/(1 + sin θ) = (sec θ - tan θ)^2`
Prove the following trigonometric identities.
`(cot A + tan B)/(cot B + tan A) = cot A tan B`
Prove the following identities:
sec2 A . cosec2 A = tan2 A + cot2 A + 2
Write the value of sin A cos (90° − A) + cos A sin (90° − A).
If \[\cos A = \frac{7}{25}\] find the value of tan A + cot A.
The value of sin2 29° + sin2 61° is
If cos A + cos2 A = 1, then sin2 A + sin4 A =
If a cos θ − b sin θ = c, then a sin θ + b cos θ =
Prove the following identity :
`(tanθ + secθ - 1)/(tanθ - secθ + 1) = (1 + sinθ)/(cosθ)`
Prove the following identity :
`(1 + cosA)/(1 - cosA) = (cosecA + cotA)^2`
Prove the following identity :
`1/(tanA + cotA) = sinAcosA`
Prove that:
tan (55° + x) = cot (35° – x)
Prove that `(sin (90° - θ))/cos θ + (tan (90° - θ))/cot θ + (cosec (90° - θ))/sec θ = 3`.
If A + B = 90°, show that `(sin B + cos A)/sin A = 2tan B + tan A.`
Prove the following identities.
`sqrt((1 + sin theta)/(1 - sin theta)` = sec θ + tan θ
The value of sin2θ + `1/(1 + tan^2 theta)` is equal to
Proved that `(1 + secA)/secA = (sin^2A)/(1 - cos A)`.
