Given that sin(A+B)=sinA cosB+coAsinB ,find the …
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Sia ? 6 years, 3 months ago
According to question we have sin (A+B) = sin A cos B + cos A sin B, we need to find the value of {tex}\sin 75 ^ { \circ }{/tex}.
Putting {tex}A = 45 ^ { \circ }{/tex} and {tex}B = 30 ^ { \circ }{/tex} in sin (A+B) = sin A cos B + cos A sin B,
we get
{tex}\sin \left( 45 ^ { \circ } + 30 ^ { \circ } \right){/tex}
{tex}= \sin 45 ^ { \circ } \cos 30 ^ { \circ } + \cos 45 ^ { \circ } \sin 30 ^ { \circ }{/tex}
{tex}\Rightarrow \sin 75 ^ { \circ }{/tex} {tex}= \frac { 1 } { \sqrt { 2 } } \times \frac { \sqrt { 3 } } { 2 } + \frac { 1 } { \sqrt { 2 } } \times \frac { 1 } { 2 }{/tex}
{tex}= \frac { \sqrt { 3 } } { 2 \sqrt { 2 } } + \frac { 1 } { 2 \sqrt { 2 } }{/tex}
{tex}= \frac { \sqrt { 3 } + 1 } { 2 \sqrt { 2 } }{/tex}
0Thank You