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

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

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

prove

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

True

Solution steps

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

Manipulating left side

sin (- x) - cos (- 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)

Manipulating right side

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

Simplify

= - cos (x) - sin (x)

We showed that the two sides could take the same form

\Rightarrow True

1 - \frac{cos ^{2} ( u )}{1 - sin ( u )} = - sin (u)

sin^{2} (t) = \frac{1 - cos ( 2 t )}{2}

tan (1 5^{\circ}) = tan (4 5^{\circ} - 3 0^{\circ})

sec (x) sin (2 x) = 2 sin (x)

sec (x) cot (x) - cot (x) cos (x) = sin (x)

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