One value of θ which satisfies the equation sin^4 θ – 2sin^2 θ – 1 lies between 0 and 2π.

Question

State whether the statement is True or False? Also give justification.

One value of θ which satisfies the equation sin⁴θ – 2sin²θ – 1 lies between 0 and 2π.

Answer 1

False

Explanation:

We have, sin⁴θ – 2sin²θ – 1 = 0

Now,

⇒ sin²θ = 1±√2

⇒ sin²θ = 1+√2 or 1-√2

We know that, -1≤ sin θ ≤ 1

⇒ sin²θ ≤ 1

but sin²θ = 1+√2 or 1-√2

Which is not possible.

Hence, the above statement is false.