Advertisements
Advertisements
Question
If sin θ + sin2 θ = 1 show that: cos2 θ + cos4 θ = 1
Advertisements
Solution
sin θ + sin2 θ = 1 ......[Given]
∴ sin θ = 1 − sin2 θ
∴ sin θ = cos2 θ ......[∵ 1 − sin2 θ = cos2 θ]
∴ sin2 θ = cos4 θ ......[Squaring both the sides]
∴ 1 − cos2 θ = cos4 θ ......[∵ sin2 θ = 1 − cos2 θ]
∴ 1 = cos2 θ + cos4 θ
∴ cos2 θ + cos4 θ = 1
APPEARS IN
RELATED QUESTIONS
Prove that sin6θ + cos6θ = 1 – 3 sin2θ. cos2θ.
Prove the following trigonometric identities.
`tan theta + 1/tan theta` = sec θ.cosec θ
`Prove the following trigonometric identities.
`(sec A - tan A)^2 = (1 - sin A)/(1 + sin A)`
Prove the following trigonometric identities.
`(1 + tan^2 A) + (1 + 1/tan^2 A) = 1/(sin^2 A - sin^4 A)`
Prove that:
(sec A − tan A)2 (1 + sin A) = (1 − sin A)
Prove the following identities:
cosec4 A (1 – cos4 A) – 2 cot2 A = 1
Prove the following identities:
`(1 + tan theta + cot theta)(sin theta - cos theta) = ((sec theta)/("cosec"^2 theta) - ("cosec" theta)/(sec^2 theta))`
If `( cos theta + sin theta) = sqrt(2) sin theta , " prove that " ( sin theta - cos theta ) = sqrt(2) cos theta`
Prove the following identity :
`(tanθ + secθ - 1)/(tanθ - secθ + 1) = (1 + sinθ)/(cosθ)`
Prove the following identity :
`(cosecθ)/(tanθ + cotθ) = cosθ`
Prove the following identity :
`2(sin^6θ + cos^6θ) - 3(sin^4θ + cos^4θ) + 1 = 0`
Without using trigonometric table , evaluate :
`cos90^circ + sin30^circ tan45^circ cos^2 45^circ`
Find x , if `cos(2x - 6) = cos^2 30^circ - cos^2 60^circ`
Prove that `((1 + sin θ - cos θ)/( 1 + sin θ + cos θ))^2 = (1 - cos θ)/(1 + cos θ)`.
Proved that cosec2(90° - θ) - tan2 θ = cos2(90° - θ) + cos2 θ.
a cot θ + b cosec θ = p and b cot θ + a cosec θ = q then p2 – q2 is equal to
Prove that cosec θ – cot θ = `(sin θ)/(1 + cos θ)`.
If cos 9α = sin α and 9α < 90°, then the value of tan 5α is ______.
If a sinθ + b cosθ = c, then prove that a cosθ – b sinθ = `sqrt(a^2 + b^2 - c^2)`.
Prove that `(cot A - cos A)/(cot A + cos A) = (cos^2 A)/(1 + sin A)^2`
