Advertisements
Advertisements
प्रश्न
sec4 A − sec2 A is equal to
पर्याय
tan2 A − tan4 A
tan4 A − tan2 A
tan4 A + tan2 A
tan2 A + tan4 A
Advertisements
उत्तर
The given expression is .`sec^4 A-sec^2A`
Taking common `sec^2 A` from both the terms, we have
`Sec^4 A-sec^2 A`
= `sec^2 A (sec^2 A-1)`
= `(1+tan^2 A)tan^2 A`
=`tan^2 A+tan^4 A`
APPEARS IN
संबंधित प्रश्न
Prove the following trigonometric identities.
sin2 A cot2 A + cos2 A tan2 A = 1
Prove the following trigonometric identities
`(1 + tan^2 theta)/(1 + cot^2 theta) = ((1 - tan theta)/(1 - cot theta))^2 = tan^2 theta`
Prove the following trigonometric identity.
`(sin theta - cos theta + 1)/(sin theta + cos theta - 1) = 1/(sec theta - tan theta)`
Prove the following trigonometric identities.
`(cot^2 A(sec A - 1))/(1 + sin A) = sec^2 A ((1 - sin A)/(1 + sec A))`
Prove the following identities:
(cosec A + sin A) (cosec A – sin A) = cot2 A + cos2 A
Prove the following identities:
`(1 - sinA)/(1 + sinA) = (secA - tanA)^2`
If x cos A + y sin A = m and x sin A – y cos A = n, then prove that : x2 + y2 = m2 + n2
`tan theta /((1 - cot theta )) + cot theta /((1 - tan theta)) = (1+ sec theta cosec theta)`
`sqrt((1+sin theta)/(1-sin theta)) = (sec theta + tan theta)`
If `(x/a sin a - y/b cos theta) = 1 and (x/a cos theta + y/b sin theta ) =1, " prove that "(x^2/a^2 + y^2/b^2 ) =2`
Write the value of `3 cot^2 theta - 3 cosec^2 theta.`
Prove the following identity :
`sin^2Acos^2B - cos^2Asin^2B = sin^2A - sin^2B`
Prove the following identity :
`1/(sinA + cosA) + 1/(sinA - cosA) = (2sinA)/(1 - 2cos^2A)`
Given `cos38^circ sec(90^circ - 2A) = 1` , Find the value of <A
Prove the following identities.
`costheta/(1 + sintheta)` = sec θ – tan θ
Prove the following identities.
`(sin^3"A" + cos^3"A")/(sin"A" + cos"A") + (sin^3"A" - cos^3"A")/(sin"A" - cos"A")` = 2
If `cos theta/(1 + sin theta) = 1/"a"`, then prove that `("a"^2 - 1)/("a"^2 + 1)` = sin θ
Prove the following:
`1 + (cot^2 alpha)/(1 + "cosec" alpha)` = cosec α
If 2sin2θ – cos2θ = 2, then find the value of θ.
If a sinθ + b cosθ = c, then prove that a cosθ – b sinθ = `sqrt(a^2 + b^2 - c^2)`.
