Question

check my work????/?

Answer 1

\(\Large \sin x \cos \dfrac{\pi}{4} + \cos x \sin \dfrac{\pi}{4} - (\sin x \cos \dfrac{\pi}{4} - \cos x \sin \dfrac{\pi}{4})=1\)

\(\Large \sin x \cos \dfrac{\pi}{4} + \cos x \sin \dfrac{\pi}{4} \color{red}{-} (\sin x \cos \dfrac{\pi}{4} \color{red}{-} \cos x \sin \dfrac{\pi}{4})=1\)

\(\Large \sin x \cos \dfrac{\pi}{4} + \cos x \sin \dfrac{\pi}{4} -\sin x \cos \dfrac{\pi}{4} \color{red}{+} \cos x \sin \dfrac{\pi}{4}=1\)

\(\Large \cancel{\sin x \cos \dfrac{\pi}{4}} + \cos x \sin \dfrac{\pi}{4} \cancel{-\sin x \cos \dfrac{\pi}{4}} + \cos x \sin \dfrac{\pi}{4}=1\)

\(\Large 2\cos x \sin \dfrac{\pi}{4} =1\)

\(\Large 2 \times \dfrac{\sqrt 2}{2} \cos x =1\)

\(\Large \sqrt 2 \cos x =1\)

\(\Large \cos x = \dfrac{1}{\sqrt 2}\)

\(\Large \cos x = \dfrac{\sqrt 2}{2}\)

Answer 2

The right side of all lines above is just 1.

Answer 3

You made an error with a sign early on.
See what I wrote in red above.

Answer 4

You are subtracting the sin of a difference which is a subtraction, so it needs to be in parentheses. Then the second sign becomes positive.

Answer 5

thsnk you so much

Answer 6

You're welcome.