Advertisements
Advertisements
प्रश्न
If `cosec theta = 2x and cot theta = 2/x ," find the value of" 2 ( x^2 - 1/ (x^2))`
Advertisements
उत्तर
2 `(x^2 - 1/(x^2))`
=`4/2(x^2 - 1/(x^2))`
=`1/2(4x^2 - 4/(x^2))`
=`1/2 [(2x)^2- (2/x)^2]`
=`1/2 [( cosec theta )^2 - (cot theta)^2]`
=`1/2 (cosec ^2 theta - cot^2 theta)`
=`1/2 (1)`
=`1/2`
APPEARS IN
संबंधित प्रश्न
Prove the following trigonometric identities:
`(1 - cos^2 A) cosec^2 A = 1`
Prove the following trigonometric identities.
`(1 + cos A)/sin^2 A = 1/(1 - cos A)`
Prove that:
`tanA/(1 - cotA) + cotA/(1 - tanA) = secA "cosec" A + 1`
Prove that:
2 sin2 A + cos4 A = 1 + sin4 A
If sec2 θ (1 + sin θ) (1 − sin θ) = k, then find the value of k.
If a cos θ + b sin θ = m and a sin θ − b cos θ = n, then a2 + b2 =
(sec A + tan A) (1 − sin A) = ______.
If cos \[9\theta\] = sin \[\theta\] and \[9\theta\] < 900 , then the value of tan \[6 \theta\] is
Prove the following identity :
cosecθ(1 + cosθ)(cosecθ - cotθ) = 1
Prove the following identity :
`((1 + tan^2A)cotA)/(cosec^2A) = tanA`
Prove the following identity :
`(cosecA)/(cosecA - 1) + (cosecA)/(cosecA + 1) = 2sec^2A`
Prove the following identity :
`sec^4A - sec^2A = sin^2A/cos^4A`
Without using trigonometric table , evaluate :
`cosec49°cos41° + (tan31°)/(cot59°)`
Without using trigonometric table , evaluate :
`sin72^circ/cos18^circ - sec32^circ/(cosec58^circ)`
Without using trigonometric identity , show that :
`sec70^circ sin20^circ - cos20^circ cosec70^circ = 0`
Prove that cot θ. tan (90° - θ) - sec (90° - θ). cosec θ + 1 = 0.
Prove the following identities.
`(cot theta - cos theta)/(cot theta + cos theta) = ("cosec" theta - 1)/("cosec" theta + 1)`
Prove that cosec θ – cot θ = `sin theta/(1 + cos theta)`
If sin θ + cos θ = p and sec θ + cosec θ = q, then prove that q(p2 – 1) = 2p.
