State whether the following are true or false. Justify your answer.
$\sin (A+B)=\sin A+\sin B$
State whether the following are true or false. Justify your answer.
$\sin (A+B)=\sin A+\sin B$
$\sin (A+B)=\sin A+\sin B$
Let $A=30^{\circ}$ and $B=60^{\circ}$
$\sin (A+B)=\sin \left(30^{\circ}+60^{\circ}\right)$
$=\sin 90^{\circ}$
$=1$
$\sin A+\sin B=\sin 30^{\circ}+\sin 60^{\circ}$
$=\frac{1}{2}+\frac{\sqrt{3}}{2}=\frac{1+\sqrt{3}}{2}$
Clearly, $\sin (A+B) \neq \sin A+\sin B$
Hence, the given statement is false.
Similar Questions
Express the ratios $\cos A ,$ tan $A$ and $\sec A$ in terms of $\sin A .$
Express the ratios $\cos A ,$ tan $A$ and $\sec A$ in terms of $\sin A .$
Evaluate the following:
$2 \tan ^{2} 45^{\circ}+\cos ^{2} 30^{\circ}-\sin ^{2} 60^{\circ}$
Evaluate the following:
$2 \tan ^{2} 45^{\circ}+\cos ^{2} 30^{\circ}-\sin ^{2} 60^{\circ}$
Given $\sec \theta=\frac{13}{12},$ calculate all other trigonometric ratios.
Given $\sec \theta=\frac{13}{12},$ calculate all other trigonometric ratios.
If $\sec 4 A =\operatorname{cosec}\left( A -20^{\circ}\right),$ where $4 A$ is an acute angle, find the value of $A$. (in $^{\circ}$)
If $\sec 4 A =\operatorname{cosec}\left( A -20^{\circ}\right),$ where $4 A$ is an acute angle, find the value of $A$. (in $^{\circ}$)
$\frac{1-\tan ^{2} 45^{\circ}}{1+\tan ^{2} 45^{\circ}}=$
$\frac{1-\tan ^{2} 45^{\circ}}{1+\tan ^{2} 45^{\circ}}=$