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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
