Advertisements
Advertisements
प्रश्न
If sin θ + sin2 θ = 1, then cos2 θ + cos4 θ =
पर्याय
−1
1
0
None of these
Advertisements
उत्तर
Given:
`sin θ+sin^2θ=1`
`⇒ 1-sin^2θ= sin θ`
Now,
`cos^2θ+cos^4θ`
`= cos^2 θ+cos^2θcos^2θ`
=` cos^2θ+(1-sin^2θ)(1-sin^2θ)`
`=cos^2θ+sinθ sinθ`
`=cos^2 θ+sin^2θ`
`=1`
APPEARS IN
संबंधित प्रश्न
Prove that:
sec2θ + cosec2θ = sec2θ x cosec2θ
Prove the following trigonometric identities.
`(sec A - tan A)/(sec A + tan A) = (cos^2 A)/(1 + sin A)^2`
Prove the following trigonometric identities.
`(cot A - cos A)/(cot A + cos A) = (cosec A - 1)/(cosec A + 1)`
Prove the following identities:
(cos A + sin A)2 + (cos A – sin A)2 = 2
Prove the following identities:
`(cotA + cosecA - 1)/(cotA - cosecA + 1) = (1 + cosA)/sinA`
Prove the following identities:
`(costhetacottheta)/(1 + sintheta) = cosectheta - 1`
If `cosA/cosB = m` and `cosA/sinB = n`, show that : (m2 + n2) cos2 B = n2.
`(sec^2 theta -1)(cosec^2 theta - 1)=1`
`tan theta/(1+ tan^2 theta)^2 + cottheta/(1+ cot^2 theta)^2 = sin theta cos theta`
`sqrt((1-cos theta)/(1+cos theta)) = (cosec theta - cot theta)`
Prove that:
`(sin^2θ)/(cosθ) + cosθ = secθ`
If a cot θ + b cosec θ = p and b cot θ − a cosec θ = q, then p2 − q2
Prove the following identity :
`sqrt((1 + sinq)/(1 - sinq)) + sqrt((1- sinq)/(1 + sinq))` = 2secq
If x = asecθ + btanθ and y = atanθ + bsecθ , prove that `x^2 - y^2 = a^2 - b^2`
If tan θ = 2, where θ is an acute angle, find the value of cos θ.
Prove that `sin A/(sec A + tan A - 1) + cos A/(cosec A + cot A - 1) = 1`.
Prove that `(tan^2 theta - 1)/(tan^2 theta + 1)` = 1 – 2 cos2θ
Choose the correct alternative:
1 + cot2θ = ?
If cos A = `(2sqrt("m"))/("m" + 1)`, then prove that cosec A = `("m" + 1)/("m" - 1)`
If 1 + sin2θ = 3 sin θ cos θ, then prove that tan θ = 1 or `1/2`.
