State whether the following are true or false. Justify your answer.
$\sin \theta=\cos \theta$ for all values of $\theta$
State whether the following are true or false. Justify your answer.
$\sin \theta=\cos \theta$ for all values of $\theta$
$\sin \theta=\cos \theta$ 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.
Similar Questions
If $\sin A =\frac{3}{4},$ calculate $\cos A$ and $\tan A$.
If $\sin A =\frac{3}{4},$ calculate $\cos A$ and $\tan A$.
$\frac{1+\tan ^{2} A}{1+\cot ^{2} A}=........$
$\frac{1+\tan ^{2} A}{1+\cot ^{2} A}=........$
If $\cot \theta=\frac{7}{8},$ evaluate:
$(i)$ $\frac{(1+\sin \theta)(1-\sin \theta)}{(1+\cos \theta)(1-\cos \theta)}$
$(ii)$ $\cot ^{2} \theta$
If $\cot \theta=\frac{7}{8},$ evaluate:
$(i)$ $\frac{(1+\sin \theta)(1-\sin \theta)}{(1+\cos \theta)(1-\cos \theta)}$
$(ii)$ $\cot ^{2} \theta$
$\sin 2 A=2 \sin A$ is true when $A=$
$\sin 2 A=2 \sin A$ is true when $A=$
Evaluate:
$\cos 48^{\circ}-\sin 42^{\circ}$
Evaluate:
$\cos 48^{\circ}-\sin 42^{\circ}$