If $A , B$ and $C$ are interior angles of a triangle $ABC ,$ then show that
$\sin \left(\frac{B+C}{2}\right)=\cos \frac{A}{2}$
If $A , B$ and $C$ are interior angles of a triangle $ABC ,$ then show that
$\sin \left(\frac{B+C}{2}\right)=\cos \frac{A}{2}$
We know that for a triangle $ABC$
$\angle A+\angle B+\angle C=180^{\circ}$
$\angle B+\angle C=180^{\circ}-\angle A$
$\frac{\angle B+\angle C}{2}=90^{\circ}-\frac{\angle A}{2}$
$\sin \left(\frac{B+C}{2}\right)=\sin \left(90^{\circ}-\frac{A}{2}\right)$
$=\cos \left(\frac{ A }{2}\right)$
Similar Questions
Prove the following identities, where the angles involved are acute angles for which the expressions are defined.
$\sqrt{\frac{1+\sin A }{1-\sin A }}=\sec A +\tan A$
Prove the following identities, where the angles involved are acute angles for which the expressions are defined.
$\sqrt{\frac{1+\sin A }{1-\sin A }}=\sec A +\tan A$
Evaluate:
$\frac{\sin 18^{\circ}}{\cos 72^{\circ}}$
Evaluate:
$\frac{\sin 18^{\circ}}{\cos 72^{\circ}}$
Evaluate the following:
$2 \tan ^{2} 45^{\circ}+\cos ^{2} 30^{\circ}-\sin ^{2} 60^{\circ}$
Evaluate the following:
$2 \tan ^{2} 45^{\circ}+\cos ^{2} 30^{\circ}-\sin ^{2} 60^{\circ}$
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:
$(i)$ $\sin A \cos C+\cos A \sin C$
$(ii)$ $\cos A \cos C-\sin A \sin C$