Advertisements
Advertisements
प्रश्न
Prove the following identity :
`cosA/(1 - tanA) + sinA/(1 - cotA) = sinA + cosA`
उत्तर
LHS = `cosA/(1 - tanA) + sinA/(1 - cotA)`
= `cosA/(1-sinA/cosA) + sinA/(1 - cosA/sinA) = cosA/((cosA -sinA)/cosA) + sinA/((sinA - cosA)/sinA)`
= `cos^2A/(cosA - sinA) + sin^2A/(sinA - cosA) = (cos^2A - sin^2A)/((cosA - sinA))`
`((cosA - sinA)(cosA + sinA))/(cosA - sinA)`
= sinA + cosA = RHS
APPEARS IN
संबंधित प्रश्न
Prove the following trigonometric identities.
`(1 + sec theta)/sec theta = (sin^2 theta)/(1 - cos theta)`
Prove the following trigonometric identities.
`(cosec A)/(cosec A - 1) + (cosec A)/(cosec A = 1) = 2 sec^2 A`
Prove the following identities:
sec2 A + cosec2 A = sec2 A . cosec2 A
Prove the following identities:
cot2 A – cos2 A = cos2 A . cot2 A
Prove that:
cos A (1 + cot A) + sin A (1 + tan A) = sec A + cosec A
If sin θ + sin2 θ = 1, then cos2 θ + cos4 θ =
Choose the correct alternative:
1 + tan2 θ = ?
Express (sin 67° + cos 75°) in terms of trigonometric ratios of the angle between 0° and 45°.
If a cos θ – b sin θ = c, then prove that (a sin θ + b cos θ) = `± sqrt("a"^2 + "b"^2 -"c"^2)`
Prove that `sintheta/(sectheta+ 1) +sintheta/(sectheta - 1)` = 2 cot θ
