Advertisements
Advertisements
प्रश्न
If cos A + cos2 A = 1, then sin2 A + sin4 A =
पर्याय
−1
0
1
None of these
उत्तर
Given:
`cos A+cos^2 A=1`
`⇒ 1- cos^2 A= cos A`
So,
`sin^2 A+sin^4 A`
`= sin^2 A+sin^2 A sin^2 A`
`= sin^2 A+(1-cos^2 A)(1-cos^2 A)`
`=sin^2 A+cos A cos A`
`=sin^2 A+cos^2 A`
`=1`
APPEARS IN
संबंधित प्रश्न
Prove that sin6θ + cos6θ = 1 – 3 sin2θ. cos2θ.
(1 + tan θ + sec θ) (1 + cot θ − cosec θ) = ______.
Prove the following trigonometric identities.
(1 + cot A − cosec A) (1 + tan A + sec A) = 2
Prove the following trigonometric identities.
`(cos A cosec A - sin A sec A)/(cos A + sin A) = cosec A - sec A`
If cos θ + cot θ = m and cosec θ – cot θ = n, prove that mn = 1
If x = a sec θ cos ϕ, y = b sec θ sin ϕ and z = c tan θ, show that `x^2/a^2 + y^2/b^2 - x^2/c^2 = 1`
Prove the following identities:
`(cotA - cosecA)^2 = (1 - cosA)/(1 + cosA)`
Prove that:
(sin A + cos A) (sec A + cosec A) = 2 + sec A cosec A
cosec4θ − cosec2θ = cot4θ + cot2θ
` (sin theta + cos theta )/(sin theta - cos theta ) + ( sin theta - cos theta )/( sin theta + cos theta) = 2/ ((1- 2 cos^2 theta))`
If `( cos theta + sin theta) = sqrt(2) sin theta , " prove that " ( sin theta - cos theta ) = sqrt(2) cos theta`
If `cos theta = 7/25 , "write the value of" ( tan theta + cot theta).`
2 (sin6 θ + cos6 θ) − 3 (sin4 θ + cos4 θ) is equal to
If a cos θ − b sin θ = c, then a sin θ + b cos θ =
Prove the following identity :
cosecθ(1 + cosθ)(cosecθ - cotθ) = 1
Without using trigonometric identity , show that :
`tan10^circ tan20^circ tan30^circ tan70^circ tan80^circ = 1/sqrt(3)`
Prove that:
`sqrt((sectheta - 1)/(sec theta + 1)) + sqrt((sectheta + 1)/(sectheta - 1)) = 2cosectheta`
Prove that: `(1 + cot^2 θ/(1 + cosec θ)) = cosec θ`.
If cosec A – sin A = p and sec A – cos A = q, then prove that `("p"^2"q")^(2/3) + ("pq"^2)^(2/3)` = 1
Proved that `(1 + secA)/secA = (sin^2A)/(1 - cos A)`.
