Is cos(-x)+sin(-x)=cos(x)-sin(x) ?

The answer to whether cos(-x)+sin(-x)=cos(x)-sin(x) is True

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prove cos(-x)+sin(-x)=cos(x)-sin(x)

prove

cos (- x) + sin (- x) = cos (x) - sin (x)

True

Solution steps

cos (- x) + sin (- x) = cos (x) - sin (x)

Manipulating left side

cos (- x) + sin (- x)

Use the negative angle identity:

sin (- x) = - sin (x)

= cos (- x) - sin (x)

Use the negative angle identity:

cos (- x) = cos (x)

= cos (x) - sin (x)

We showed that the two sides could take the same form

\Rightarrow True

\frac{1 - cos ( 2 θ )}{cos ( 2 θ ) + 1} = tan^{2} (θ)

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

\frac{sin ( y )}{cot ( y )} = sec (y) - cos (y)

cos (x) - sin (x) = 2 \cdot cos (x + \frac{π}{4})

sin^{4} (θ) - 2 sin^{2} (θ) = cos^{4} (θ) - 1

Is cos(-x)+sin(-x)=cos(x)-sin(x) ?
The answer to whether cos(-x)+sin(-x)=cos(x)-sin(x) is True