Question

sin 67*1/2+cos67*1/2=??

Answer 1

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Answer 2

Answer:

$\sin (67\frac{1}{2})+\cos (67\frac{1}{2})=\frac{1}{2\sqrt2}$

Step-by-step explanation:

Given : Expression $\sin (67\frac{1}{2})+\cos (67\frac{1}{2})$

To find : Solve the expression?

Solution :

Expression $\sin (67.5)+\cos (67.5)$

Multiply and divide by 2,

$=\frac{2\sin (67.5)+\cos (67.5)}{2}$

We know, $2\sin A\cos A=\sin 2A$

$=\frac{\sin (2\times 67.5)}{2}$

$=\frac{\sin (135)}{2}$

$=\frac{1}{2}\times \sin(90+45)$

$=\frac{1}{2}\times \cos(45)$

$=\frac{1}{2}\times \frac{1}{\sqrt2}$

$=\frac{1}{2\sqrt2}$

Therefore, $\sin (67\frac{1}{2})+\cos (67\frac{1}{2})=\frac{1}{2\sqrt2}$