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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.
Options
True
False
Solution
This statement is False.
Explanation:
Given equation is sin4θ – 2sin2θ – 1 = 0
sin2θ = `(-(-2) +- sqrt((-2)^2 - 4 xx 1 xx -1))/(2 xx 1)`
= `(2 +- sqrt(4 + 4))/2`
= `(2 +- sqrt(8))/2`
= `(2 +- 2sqrt(2))/2`
= `1 +- sqrt(2)`
∴ sin2θ = `(1 + sqrt(2))` or `(1 - sqrt(2))`
⇒ – 1 ≤ sin θ ≤ 1
⇒ sin2θ ≤ 1 but sin2θ = `(1 + sqrt(2))` or `(1 - sqrt(2))`
Which is not possible.
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