Advertisements
Advertisements
प्रश्न
Prove the following trigonometric identities.
`(1 - tan^2 A)/(cot^2 A -1) = tan^2 A`
उत्तर
`(1 - sin^2 A/cos^2 A)/(cos^2 A/sin^2 A -1) = ((cos^2 A - sin^2 A)/cos^2 A)/((cos^2 A - sin^2 A)/sin^2 A`
`= (sin^2 A)/cos^2 A`
`= tan^2 A`
APPEARS IN
संबंधित प्रश्न
Prove the following trigonometric identities.
`cos theta/(1 + sin theta) = (1 - sin theta)/cos theta`
Prove the following trigonometric identities.
`tan theta/(1 - cot theta) + cot theta/(1 - tan theta) = 1 + tan theta + cot theta`
Prove the following trigonometric identities.
`(1/(sec^2 theta - cos theta) + 1/(cosec^2 theta - sin^2 theta)) sin^2 theta cos^2 theta = (1 - sin^2 theta cos^2 theta)/(2 + sin^2 theta + cos^2 theta)`
Prove the following identities:
`(1 - sinA)/(1 + sinA) = (secA - tanA)^2`
Prove that:
(sec A − tan A)2 (1 + sin A) = (1 − sin A)
Prove the following identities:
`cosecA - cotA = sinA/(1 + cosA)`
\[\frac{x^2 - 1}{2x}\] is equal to
If cos A + cos2 A = 1, then sin2 A + sin4 A =
If a cos θ − b sin θ = c, then a sin θ + b cos θ =
Prove the following identity :
`sec^4A - sec^2A = sin^2A/cos^4A`
If `asin^2θ + bcos^2θ = c and p sin^2θ + qcos^2θ = r` , prove that (b - c)(r - p) = (c - a)(q - r)
Without using trigonometric table , evaluate :
`sin72^circ/cos18^circ - sec32^circ/(cosec58^circ)`
Without using trigonometric identity , show that :
`tan10^circ tan20^circ tan30^circ tan70^circ tan80^circ = 1/sqrt(3)`
If tan θ = 2, where θ is an acute angle, find the value of cos θ.
Prove that: `(sec θ - tan θ)/(sec θ + tan θ ) = 1 - 2 sec θ.tan θ + 2 tan^2θ`
Proved that cosec2(90° - θ) - tan2 θ = cos2(90° - θ) + cos2 θ.
Prove that: sin4 θ + cos4θ = 1 - 2sin2θ cos2 θ.
Prove that
sin2A . tan A + cos2A . cot A + 2 sin A . cos A = tan A + cot A
Prove the following:
`tanA/(1 + sec A) - tanA/(1 - sec A)` = 2cosec A
`1/sin^2θ - 1/cos^2θ - 1/tan^2θ - 1/cot^2θ - 1/sec^2θ - 1/("cosec"^2θ) = -3`, then find the value of θ.
