Advertisements
Advertisements
Question
If sinθ + sin2 θ = 1, prove that cos2 θ + cos4 θ = 1
Advertisements
Solution
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
RELATED QUESTIONS
Prove the following trigonometric identities.
tan2θ cos2θ = 1 − cos2θ
Prove the following trigonometric identities.
`1/(1 + sin A) + 1/(1 - sin A) = 2sec^2 A`
If cos θ + cos2 θ = 1, prove that sin12 θ + 3 sin10 θ + 3 sin8 θ + sin6 θ + 2 sin4 θ + 2 sin2 θ − 2 = 1
If m = a sec A + b tan A and n = a tan A + b sec A, then prove that : m2 – n2 = a2 – b2
If `cosA/cosB = m` and `cosA/sinB = n`, show that : (m2 + n2) cos2 B = n2.
Prove the following identities:
`sqrt((1 + sinA)/(1 - sinA)) = cosA/(1 - sinA)`
`sin^2 theta + 1/((1+tan^2 theta))=1`
If \[\sin \theta = \frac{4}{5}\] what is the value of cotθ + cosecθ?
Prove that sin θ sin( 90° - θ) - cos θ cos( 90° - θ) = 0
Prove that sin (90° - θ) cos (90° - θ) = tan θ. cos2θ.
