State whether following are true or false. Justify your answer. sin θ=cos θ for all values of θ

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8. Introduction to Trigonometry

easy

State whether the following are true or false. Justify your answer.

$\sin \theta=\cos \theta$ for all values of $\theta$

Option A

Option B

Option C

Option D

Solution

$\sin \theta=\cos \theta$ for all values of $\theta$

This is true when $\theta=45^{\circ}$

As $\sin 45^{\circ}=\frac{1}{\sqrt{2}}$

$\cos 45^{\circ}=\frac{1}{\sqrt{2}}$

It is not true for all other values of $\theta$.

$\sin 30^{\circ}=\frac{1}{2}$ and $\cos 30^{\circ}=\frac{\sqrt{3}}{2}$

Hence, the given statement is false.

Standard 10

Mathematics

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