Question

Please help me with this question I don’t understand and been struggling would love to appreciate your help this is not test or anything it’s just Hw thank you!

Answer 1

we have the expression

`\sin (x-(\pi)/(4))=\frac{\sqrt[]{2}}{2}(\sin x-\cos x)`

Remember that

`\sin (x-(\pi)/(4))=\sin x\cdot\cos (\pi)/(4)-\cos x\cdot\sin (\pi)/(4)`

and

`\cos (\pi)/(4)=\sin (\pi)/(4)=\frac{\sqrt[]{2}}{2}`

substitute

`\sin (x-(\pi)/(4))=\sin x\cdot\frac{\sqrt[]{2}}{2}-\cos x\cdot\frac{\sqrt[]{2}}{2}`

Factor

`\sin (x-(\pi)/(4))=\frac{\sqrt[]{2}}{2}\cdot(\sin x-\cos x)`

therefore

The identity is verified

the answer in the blank box must be

`\sin x\cdot\cos (\pi)/(4)-\cos x\cdot\sin (\pi)/(4)`