If sin θ + sin2 = 1, then cos2θ + cos4θ =

Given: sin θ + sin2 θ = 1⇒ sin θ = 1 – sin2 θ = cos2 θ [∵ sin2 θ + cos2 θ = 1]……(i)⇒ Sin2 θ = (cos2 θ)2 = cos4 θ ……(ii)To find: cos2 θ + cos4 θConsider cos2 θ + cos4 θ = sin θ + sin2 θ [Using (i) and (ii)]= 1 [Given]

Q. 204.1( 14 Votes )

If sin θ + sin² = 1, then cos²θ + cos⁴θ =
A. −1

B. 1

C. 0

D. None of these

Class 10th RD Sharma - Mathematics 6. Trigonometric Identities

Answer :

Given: sin θ + sin² θ = 1

⇒ sin θ = 1 – sin² θ = cos² θ [∵ sin² θ + cos² θ = 1]……(i)

⇒ Sin² θ = (cos² θ)² = cos⁴ θ ……(ii)

To find: cos² θ + cos⁴ θ

Consider cos² θ + cos⁴ θ = sin θ + sin² θ [Using (i) and (ii)]

= 1 [Given]

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If sin θ + sin2 = 1, then cos2θ + cos4θ = A. −1B. 1C. 0D. None of these

If sin θ + sin² = 1, then cos²θ + cos⁴θ =
A. −1

B. 1

C. 0

D. None of these