Is 1+cos((3pi)/4)=1-sin((3pi)/4) ?

The answer to whether 1+cos((3pi)/4)=1-sin((3pi)/4) is True

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prove 1+cos((3pi)/4)=1-sin((3pi)/4)

prove

1 + cos (\frac{3 π}{4}) = 1 - sin (\frac{3 π}{4})

True

Solution steps

1 + cos (\frac{3 π}{4}) = 1 - sin (\frac{3 π}{4})

Manipulating left side

1 + cos (\frac{3 π}{4})

Simplify

= 1 - \frac{2}{2}

Manipulating right side

1 - sin (\frac{3 π}{4})

Simplify

= 1 - \frac{2}{2}

We showed that the two sides could take the same form

\Rightarrow True

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sin (\frac{7 π}{6} + x) - cos (\frac{2 π}{3} + x) = 0

(1 + cos (a)) (1 - cos (a)) = sin^{2} (a)

csc (θ) - cos (θ) cot (θ) = sin (θ)

sin (x + \frac{π}{3}) + sin (x - \frac{π}{3}) = sin (x)

Is 1+cos((3pi)/4)=1-sin((3pi)/4) ?
The answer to whether 1+cos((3pi)/4)=1-sin((3pi)/4) is True