Advertisements
Advertisements
प्रश्न
Prove that `(1 + sintheta)/(1 - sin theta)` = (sec θ + tan θ)2
उत्तर
L.H.S = `(1 + sintheta)/(1 - sin theta)`
= `((1 + sintheta)/(costheta))/((1 - sintheta)/(costheta))` ......[Dividing numerator and denominator by cos θ]
= `(1/costheta + (sintheta)/(costheta))/(1/costheta - (sintheta)/(costheta)`
= `(sectheta + tantheta)/(sectheta - tantheta)`
= `(sectheta + tantheta)/(sectheta - tantheta) xx (sectheta + tantheta)/(sectheta + tantheta)` ......[On rationalising the denominator]
= `(sectheta + tantheta)^2/(sec^2theta - tan^2theta)`
= `(sectheta + tantheta)^2/1` ......`[(because 1 + tan^2theta = sec^2theta),(therefore sec^2theta - tan^2theta = 1)]`
= (sec θ + tan θ)2
= R.H.S
∴ `(1 + sintheta)/(1 - sin theta)` = (sec θ + tan θ)2
APPEARS IN
संबंधित प्रश्न
Prove the following identities:
`(i) (sinθ + cosecθ)^2 + (cosθ + secθ)^2 = 7 + tan^2 θ + cot^2 θ`
`(ii) (sinθ + secθ)^2 + (cosθ + cosecθ)^2 = (1 + secθ cosecθ)^2`
`(iii) sec^4 θ– sec^2 θ = tan^4 θ + tan^2 θ`
Prove the following identities:
cot2 A – cos2 A = cos2 A . cot2 A
Prove the following identities:
`secA/(secA + 1) + secA/(secA - 1) = 2cosec^2A`
`sin theta (1+ tan theta) + cos theta (1+ cot theta) = ( sectheta+ cosec theta)`
`cot theta/((cosec theta + 1) )+ ((cosec theta +1 ))/ cot theta = 2 sec theta `
If cosec θ = 2x and \[5\left( x^2 - \frac{1}{x^2} \right)\] \[2\left( x^2 - \frac{1}{x^2} \right)\]
\[\frac{\sin \theta}{1 + \cos \theta}\]is equal to
\[\frac{\tan \theta}{\sec \theta - 1} + \frac{\tan \theta}{\sec \theta + 1}\] is equal to
Prove the following identity :
`(secA - 1)/(secA + 1) = (1 - cosA)/(1 + cosA)`
Prove the following identity :
`tan^2A - sin^2A = tan^2A.sin^2A`
Prove the following identity :
`sinA/(1 + cosA) + (1 + cosA)/sinA = 2cosecA`
Prove the following identity :
`1/(tanA + cotA) = sinAcosA`
Prove the following identity :
`1/(cosA + sinA - 1) + 2/(cosA + sinA + 1) = cosecA + secA`
Prove that `(tan^2"A")/(tan^2 "A"-1) + (cosec^2"A")/(sec^2"A"-cosec^2"A") = (1)/(1-2 co^2 "A")`
Prove that :
2(sin6 θ + cos6 θ) − 3 (sin4 θ + cos4 θ) + 1 = 0
Prove that tan2Φ + cot2Φ + 2 = sec2Φ.cosec2Φ.
Prove that sin (90° - θ) cos (90° - θ) = tan θ. cos2θ.
If 5x = sec θ and `5/x` = tan θ, then `x^2 - 1/x^2` is equal to
Prove that sin6A + cos6A = 1 – 3sin2A . cos2A
Proved that `(1 + secA)/secA = (sin^2A)/(1 - cos A)`.
