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 $\angle B$ and $\angle Q$ are acute angles such that $\sin B =\sin Q$, then prove that $\angle B =\angle Q$.
If $\angle B$ and $\angle Q$ are acute angles such that $\sin B =\sin Q$, then prove that $\angle B =\angle Q$.
$9 \sec ^{2} A-9 \tan ^{2} A=..........$
$9 \sec ^{2} A-9 \tan ^{2} A=..........$
Evaluate:
$\operatorname{cosec} 31^{\circ}-\sec 59^{\circ}$
Evaluate:
$\operatorname{cosec} 31^{\circ}-\sec 59^{\circ}$
In triangle $ABC ,$ right -angled at $B ,$ if $\tan A =\frac{1}{\sqrt{3}},$ find the value of:
$(i)$ $\sin A \cos C+\cos A \sin C$
$(ii)$ $\cos A \cos C-\sin A \sin C$
In triangle $ABC ,$ right -angled at $B ,$ if $\tan A =\frac{1}{\sqrt{3}},$ find the value of:
$(i)$ $\sin A \cos C+\cos A \sin C$
$(ii)$ $\cos A \cos C-\sin A \sin C$
Prove the following identities, where the angles involved are acute angles for which the expressions are defined.
$(\operatorname{cosec} \theta-\cot \theta)^{2}=\frac{1-\cos \theta}{1+\cos \theta}$
Prove the following identities, where the angles involved are acute angles for which the expressions are defined.
$(\operatorname{cosec} \theta-\cot \theta)^{2}=\frac{1-\cos \theta}{1+\cos \theta}$