If cos θ + cos2θ = 1, then find the value of expression (sin2θ + sin4θ).


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Answer:

1

Step by Step Explanation:
  1. It is given that
    cos θ + cos2θ = 1 ............. Eq. (1)
  2. Above equation can be re-written as following
    ⇒ 1 - cos2θ = cos θ
  3. Since 1 - cos2θ = sin2θ, we can re-write equation as following,
    ⇒ sin2θ = cos θ ............. Eq. (2)
  4. Now replace value of sin2θ = cos θ, in required expression
    sin2θ + sin4θ = cos θ + cos2θ
    ⇒ sin2θ + sin4θ = 1 .................... Using Eq. (1)

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