Trigonometrical Equations Ques 18

  1. 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: 18.False

Solution:

Formula:

Domain and Range of Trigonometric Functions:

  1. 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.



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