Advertisements
Advertisements
प्रश्न
Prove that `(sin θ tan θ)/(1 - cos θ) = 1 + sec θ.`
Advertisements
उत्तर
LHS = `( sin θ tan θ)/(1 - cos θ)`
= `(sin θ. (sin θ)/(cos θ))/(1 - cos θ)`
= `sin^2 θ/(cos θ( 1 - cos θ))`
= `((1 - cos θ)(1 + cos θ))/(cos θ(1 - cos θ))`
= `(1 + cos θ)/(cos θ) = 1/(cos θ) + cos θ/cos θ`
= sec θ + 1
= RHS
Hence proved.
संबंधित प्रश्न
Prove the following trigonometric identities.
`cot theta - tan theta = (2 cos^2 theta - 1)/(sin theta cos theta)`
Prove the following trigonometric identities.
`(1 + sec theta)/sec theta = (sin^2 theta)/(1 - cos theta)`
Prove the following identities:
`1 - sin^2A/(1 + cosA) = cosA`
`(1+ cos theta - sin^2 theta )/(sin theta (1+ cos theta))= cot theta`
If `(x/a sin a - y/b cos theta) = 1 and (x/a cos theta + y/b sin theta ) =1, " prove that "(x^2/a^2 + y^2/b^2 ) =2`
Write the value of ` cosec^2 (90°- theta ) - tan^2 theta`
Prove the following identity :
`sqrt((1 - cosA)/(1 + cosA)) = sinA/(1 + cosA)`
Prove that `tan^3 θ/( 1 + tan^2 θ) + cot^3 θ/(1 + cot^2 θ) = sec θ. cosec θ - 2 sin θ cos θ.`
Prove that `(sin θ)/(sec θ + 1) + (sin θ)/(sec θ - 1) = 2 cot θ`.
Prove the following:
`1 + (cot^2 alpha)/(1 + "cosec" alpha)` = cosec α
