Is sin(-θ)+cos(-θ)=cos(θ)-sin(θ) ?

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

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prove sin(-θ)+cos(-θ)=cos(θ)-sin(θ)

prove

sin (- θ) + cos (- θ) = cos (θ) - sin (θ)

True

Solution steps

sin (- θ) + cos (- θ) = cos (θ) - sin (θ)

Manipulating left side

sin (- θ) + cos (- θ)

Use the negative angle identity:

sin (- x) = - sin (x)

= cos (- θ) - sin (θ)

Use the negative angle identity:

cos (- x) = cos (x)

= cos (θ) - sin (θ)

We showed that the two sides could take the same form

\Rightarrow True

sec (- θ) = - sec (θ)

cot^{2} (x) = \frac{cos ^{2} ( x )}{1 - cos ^{2} ( x )}

\frac{cos ^{2} ( x ) tan ( x )}{cot ( x )} = sin^{2} (x)

\frac{tan ^{2} ( x ) + 1}{1 + cot ^{2} ( x )} = tan^{2} (x)

3 cos (3 x) = 3 cos (x) - 12 sin^{2} (x) cos (x)

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