Advertisements
Advertisements
प्रश्न
If sinθ + sin2 θ = 1, prove that cos2 θ + cos4 θ = 1
Advertisements
उत्तर
We have,
sinθ + sin2 θ = 1
⇒ sinθ = 1 – sin2 θ
⇒ sin θ = cos2 θ ......[∵ sin2 θ + cos2 θ = 1]
(sinθ)2 = (cos2 θ)2
sin2 θ = cos4 θ
= cos2 θ + cos4 θ
= sin θ + sin2 θ
cos2 θ + cos4 θ = 1
APPEARS IN
संबंधित प्रश्न
Prove the following trigonometric identities.
`tan theta + 1/tan theta` = sec θ.cosec θ
Prove the following trigonometric identities.
`(1 + cos theta - sin^2 theta)/(sin theta (1 + cos theta)) = cot theta`
Prove the following identities:
`(1 + cosA)/(1 - cosA) = tan^2A/(secA - 1)^2`
If `m = (cos θ - sin θ)` and `n = (cos θ + sin θ)`, show that `sqrt(m/n) + sqrt(n/m) = 2/sqrt(1 - tan^2θ)`.
Write the value of `sin theta cos ( 90° - theta )+ cos theta sin ( 90° - theta )`.
If `sec theta = x ,"write the value of tan" theta`.
Prove the following identity :
`(cotA + tanB)/(cotB + tanA) = cotAtanB`
If cosθ = `5/13`, then find sinθ.
Show that tan 7° × tan 23° × tan 60° × tan 67° × tan 83° = `sqrt(3)`.
Statement 1: sin2θ + cos2θ = 1
Statement 2: cosec2θ + cot2θ = 1
Which of the following is valid?
