Advertisements
Advertisements
प्रश्न
Prove the following identities.
`sqrt((1 + sin theta)/(1 - sin theta)` = sec θ + tan θ
Advertisements
उत्तर
L.H.S. = `sqrt((1 + sin theta)/(1 - sin theta)`
= `sqrt(((1 + sin theta)(1 + sin theta))/((1 - sin theta)(1 + sin theta))` ...[conjugate (1 − sin θ)]
= `sqrt((1 + sin theta)^2/(1 - sin^2 theta)`
= `sqrt((1 + sin theta)^2/(cos^2 theta)`
= `(1 + sin theta)/(cos theta)`
= `1/cos theta + sin theta/cos theta`
= sec θ + tan θ
L.H.S. = R.H.S.
APPEARS IN
संबंधित प्रश्न
Prove the following identities, where the angles involved are acute angles for which the expressions are defined:
`(cos A-sinA+1)/(cosA+sinA-1)=cosecA+cotA ` using the identity cosec2 A = 1 cot2 A.
if `cos theta = 5/13` where `theta` is an acute angle. Find the value of `sin theta`
Prove the following identities:
`(cotA - cosecA)^2 = (1 - cosA)/(1 + cosA)`
Prove the following identities:
`cotA/(1 - tanA) + tanA/(1 - cotA) = 1 + tanA + cotA`
`1+((tan^2 theta) cot theta)/(cosec^2 theta) = tan theta`
If `cos B = 3/5 and (A + B) =- 90° ,`find the value of sin A.
Write True' or False' and justify your answer the following :
The value of the expression \[\sin {80}^° - \cos {80}^°\]
Prove that: 2(sin6 θ + cos6 θ) – 3 (sin4 θ + cos4 θ) + 1 = 0.
Prove that cosec θ – cot θ = `(sin θ)/(1 + cos θ)`.
Prove the following identity:
(sin2θ – 1)(tan2θ + 1) + 1 = 0
