Advertisements
Advertisements
प्रश्न
Prove the following identities:
`(costhetacottheta)/(1 + sintheta) = cosectheta - 1`
उत्तर
L.H.S. = `(costhetacottheta)/(1 + sintheta)`
= `(costhetacottheta)/(1 + sintheta) xx (1 - sintheta)/(1 - sintheta)`
= `(costhetacottheta(1 - sintheta))/(1 - sin^2theta)`
= `(costheta costheta/sintheta(1 - sintheta))/cos^2theta`
= `(1 - sintheta)/sintheta`
= `1/sintheta - 1`
= cosec θ – 1
APPEARS IN
संबंधित प्रश्न
Prove the following trigonometric identities.
`cos theta/(1 + sin theta) = (1 - sin theta)/cos theta`
Prove the following identities:
`tan A - cot A = (1 - 2cos^2A)/(sin A cos A)`
Prove the following identities:
`(cosecA)/(cosecA - 1) + (cosecA)/(cosecA + 1) = 2sec^2A`
Prove the following identities:
`(sintheta - 2sin^3theta)/(2cos^3theta - costheta) = tantheta`
Prove that:
`1/(cosA + sinA - 1) + 1/(cosA + sinA + 1) = cosecA + secA`
`(tan theta)/((sec theta -1))+(tan theta)/((sec theta +1)) = 2 sec theta`
Prove the following identity :
`(secθ - tanθ)^2 = (1 - sinθ)/(1 + sinθ)`
Prove the following identity :
`(cos^3A + sin^3A)/(cosA + sinA) + (cos^3A - sin^3A)/(cosA - sinA) = 2`
Prove that: `sqrt((1 - cos θ)/(1 + cos θ)) = cosec θ - cot θ`.
Prove the following identities:
`1/(sin θ + cos θ) + 1/(sin θ - cos θ) = (2sin θ)/(1 - 2 cos^2 θ)`.
