Question

sin ( π÷4 + theta) =?

Answer 1

Answer:

$The \: value \: of \: \red{ Sin\left(\frac{\pi}{4} + \theta\right)} = \green { \frac{1}{\sqrt{2}}(cos\theta+sin\theta)}$

Step-by-step explanation:

$The \: value \: of \: \red{ Sin\left(\frac{\pi}{4} + \theta\right)}$

$= sin\frac{\pi}{4} cos \theta +cos\frac{\pi}{4} sin \theta$

$\boxed { \pink { sin(A+B)=sinAcosB+cosAsinB}}$

$= \frac{1}{\sqrt{2}}\times cos\theta + \frac{1}{\sqrt{2}}\times sin\theta$

$\boxed { \pink { sin\frac{\pi}{4} = cos\frac{\pi}{4} = \frac{1}{\sqrt{2}}}}$

$= \frac{1}{\sqrt{2}}(cos\theta+sin\theta)$

Therefore.,

$The \: value \: of \: \red{ Sin\left(\frac{\pi}{4} + \theta\right)} = \green { \frac{1}{\sqrt{2}}(cos\theta+sin\theta)}$

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