Sum and Difference Formulas

Question 1:

1 pts

Which identity is this?

\cos\alpha\cos\beta-\sin\alpha\sin\beta

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

Question 2:

1 pts

Which identity is this?

\sin\alpha\cos\beta-\cos\alpha\sin\beta

	The sine of angle alpha plus angle beta.
	The sine of angle alpha minus angle beta.
	The cosine of angle alpha plus angle beta.
	The tangent of angle alpha plus angle beta.

Question 3:

1 pts

\sin20^{\circ}\cdot\cos10^{\circ}+\cos20^{\circ}\cdot\sin10^{\circ}=sin(30^{\circ})=\dfrac{1}{2}

Question 4:

1 pts

\cos \dfrac{7\pi}{10}\cdot \cos\dfrac{\pi}{5}+\sin \dfrac{7\pi}{10}\cdot \sin \dfrac{\pi}{5}=1

Question 5:

2 pts

Use the angle sum identity to find the exact value of

\cos 105^{\circ}.

$\dfrac{\sqrt{2}+\sqrt{6}}{4}$	$\dfrac{-\sqrt{2}-\sqrt{6}}{4}$
$\dfrac{\sqrt{2}-\sqrt{6}}{4}$	none of these

Question 6:

2 pts

\tan\alpha=-\dfrac{3}{4}

and

\alpha \in \left(\dfrac{\pi}{2}, \pi\right)

then find the value of

\sin \left(\dfrac{\pi}{4}+\alpha\right).

Question 7:

2 pts

\sin \alpha=\sin\beta=\dfrac{5}{13}

and

\alpha \in \left(0, \dfrac{\pi}{2}\right); \beta \in \left(\dfrac{\pi}{2},\pi\right)

then find the value of

\cos(\alpha+\beta).

\cos(\alpha+\beta)=

Question 8:

2 pts

Use the angle difference identity to find

\cos(x-\pi).

$\cos x$	$-\cos x$
$\sin x$	$-\sin x$

Question 9:

3 pts

Simplify the expression.

(\sin x+\sin y)^{2}+(\cos x+ \cos y)^{2}=

Question 10:

3 pts

Simplify the expression.

\dfrac{\sin{\dfrac{\pi}{7}}\cos\dfrac{2\pi}{7}+\cos\dfrac{\pi}{7}\sin\dfrac{2\pi}{7}}{\cos\dfrac{\pi}{7}\cos\dfrac{\pi}{14}+\sin\dfrac{\pi}{7}\sin\dfrac{\pi}{14}}=

Question 11:

3 pts

Simplify the expression.

\cos \left(\dfrac{\pi}{3}-\alpha\right)=

Question 12:

3 pts

\tan \alpha=\dfrac{1}{7}

and

\alpha+\beta=\dfrac{\pi}{4}

find

\tan \beta.

\tan \beta=

Angle Measurement