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)

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

Simplify

= cos (x) + sin (x)

We showed that the two sides could take the same form

\Rightarrow True

p ro v e cos (θ) sec (θ) = 1

p ro v e cos (a + b) + cos (a - b) = 2 cos (a) cos (b)

p ro v e csc^{2} (x) - cos^{2} (x) csc^{2} (x) = 1

p ro v e tan (\frac{π}{2} - u) = cot (u)

p ro v e csc (θ) - cot (θ) = \frac{sin ( θ )}{1 + cos ( θ )}

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