If sinθ + sin2θ = 1, then cos2θ + cos4θ = ………A) -1 B) 1 C

1.	If sinθ + sin2θ = 1, then cos2θ + cos4θ = ………A) -1 B) 1 C) 0 D) None of these
Answer» Correct option is: B) 1 We have sin\(\theta\) + \(sin^2\theta\) = 1...(1) = \(1-sin^2\theta = sin\,\theta\) = \(cos^2\theta = sin\,\theta\) ...(2) (\(\because\) \(1- sin^2\theta = cos^2\theta\)) Now, \(cos^2\theta + cos^4\theta = cos^2\theta + (cos^2\theta)^2\) = sin \(\theta\) + \((sin \, \theta)^2\)(\(\because\) \(cos^2\theta = sin \theta \) from (2)) = sin \(\theta\) + \(sin^2\theta\) = 1 (From (1)) Correct option is: B) 1

If sinθ + sin2θ = 1, then cos2θ + cos4θ = ………A) -1 B) 1 C) 0 D) None of these

Answer»

Correct option is: B) 1

We have sin\(\theta\) + \(sin^2\theta\) = 1...(1)

= \(1-sin^2\theta = sin\,\theta\)

= \(cos^2\theta = sin\,\theta\) ...(2) (\(\because\) \(1- sin^2\theta = cos^2\theta\))

Now, \(cos^2\theta + cos^4\theta = cos^2\theta + (cos^2\theta)^2\)

= sin \(\theta\) + \((sin \, \theta)^2\)(\(\because\) \(cos^2\theta = sin \theta \) from (2))

= sin \(\theta\) + \(sin^2\theta\)

= 1 (From (1))

Correct option is: B) 1