Advertisements
Advertisements
प्रश्न
Prove that `(cos θ)/(1 - sin θ) = (1 + sin θ)/(cos θ)`.
Advertisements
उत्तर
L.H.S. = `cos θ/(1 - sin θ)`
= `(cos θ(1 + sin θ))/((1 - sin θ)(1 + sin θ))`
= `(cos θ(1 + sin θ))/(1 - sin^2θ)`
= `(cos θ(1 + sin θ))/(cos^2 θ)`
= `( 1 + sin θ)/cos θ`
Hence proved.
संबंधित प्रश्न
Prove the following trigonometric identities.
`sqrt((1 - cos theta)/(1 + cos theta)) = cosec theta - cot theta`
Prove the following trigonometric identities.
`(cosec A)/(cosec A - 1) + (cosec A)/(cosec A = 1) = 2 sec^2 A`
`(cos^3 θ + sin^3 θ)/(cos θ + sin θ) + (cos ^3 θ - sin^3 θ)/(cos θ - sin θ) = 2`
` (sin theta + cos theta )/(sin theta - cos theta ) + ( sin theta - cos theta )/( sin theta + cos theta) = 2/ ((1- 2 cos^2 theta))`
`(cos ec^theta + cot theta )/( cos ec theta - cot theta ) = (cosec theta + cot theta )^2 = 1+2 cot^2 theta + 2cosec theta cot theta`
Prove the following identity :
`sqrt((1 - cosA)/(1 + cosA)) = sinA/(1 + cosA)`
Prove the following identity :
`sqrt((1 + cosA)/(1 - cosA)) = cosecA + cotA`
Prove that (sin θ + cosec θ)2 + (cos θ + sec θ)2 = 7 + tan2 θ + cot2 θ.
Prove that:
`(cos^3 θ + sin^3 θ)/(cos θ + sin θ) + (cos^3 θ - sin^3 θ)/(cos θ - sin θ) = 2`
Prove that `"cosec" θ xx sqrt(1 - cos^2θ) = 1`.
