Trigonometrical Equations 1 Question 24
24. There exists a value of $\theta$ between 0 and $2 \pi$ that satisfies the equation $\sin ^{4} \theta-2 \sin ^{2} \theta+1=0$.
(1984, 1M)
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Answer:
Correct Answer: 24. $x=30^{\circ}$
Solution:
- Given, $\sin ^{4} \theta-2 \sin ^{2} \theta+1=2$
$\Rightarrow\left(\sin ^{2} \theta-1\right)^{2}=2 \quad \Rightarrow \quad \sin ^{2} \theta= \pm \sqrt{2}+1$
which is not possible. Hence, given statement is false.
