Question

Which sum or difference identity would you use to verify that cos (180° - ∅) = -cos ∅?

Answer 1

Answer: Option C is correct

Step-by-step explanation:

We know tha tCos(A-B) = cosA cosB + sinAsinB

Plugging A = 180 and B = Ф

cos(180-Ф)= cos180cosФ+sin180sinФ

                  = (-1) cosФ+ (0) sinФ   [ since cos180=-1 and sin180 =0]

                 = -cosФ + 0

                 = -cosФ

Therefore option C is the correct answer.        

Answer 2

Answer:

Option (b) is correct.

b) $\cos (\alpha-\beta)=\cos\alpha\cdot\cos\beta+\sin\alpha\cdot\sin\beta$

Step-by-step explanation:

Given $\cos (180^{\circ}-\phi)=-\cos \phi$

To prove the above stated formula we have to choose one of the identity from the given options .

Since right side of above formula is $180^{\circ}-\phi$ which is same as $\cos (\alpha-\beta)$, we will use the identity $\cos (\alpha-\beta)$

$\cos (\alpha-\beta)=\cos\alpha\cdot\cos\beta+\sin\alpha\cdot\sin\beta$

$\cos (180^{\circ}-\phi)=\cos 180^{\circ}\cdot\cos\phi+\sin 180^{\circ}\cdot\sin\phi$

We know  $\cos 180^{\circ}=-1$ and $\sin 180^{\circ}=0$

Substitute above, we get,

$\cos (180^{\circ}-\phi)=-\cos \phi$

Thus, Option (b) is correct.