Free Printable Sum and Difference Formulas

1.

Which of the following is equivalent to $\sin\left(\alpha+\beta\right)$ ?

a)

$\sin\alpha\cos\alpha+\sin\beta\cos\beta$

b)

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

c)

$\sin\alpha\cos\beta+\cos\alpha\sin\beta$

d)

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

2.

Which of the following is equivalent to $\cos\left(\alpha-\beta\right)$ ?

a)

$\cos\alpha\cos\beta+\sin\alpha\sin\beta$

b)

$\cos\alpha\cos\beta-\sin\alpha\sin B$

c)

$\cos\alpha\sin\beta+\sin\alpha\cos\beta$

d)

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

3.

Write the following expression as the sine, cosine, or tangent of an angle.
cos(175)cos(55)+sin(175)sin(55)

a)

sin(120)

b)

cos(120)

c)

cos(230)

d)

sin(230)

4.

Use Sum or Difference Identities to find the exact value of
sin(π/12)

a)

(-√(2)-√(6))/2

b)

(√(6)-√(2))/4

c)

(√(2)+√(3))/4

d)

(-√(6)+√(2))/4

5.

Use Sum or Difference Identities to find the exact value of each expression.
cos(75°)

a)

1/4

b)

( √(6) - √(2) ) / 4

c)

(√(6) + √(2)) / 4

d)

(-√(6) - √(2)) / 4

6.

How could you break up $\sin\ \frac{\pi}{12}$ to use the sum or difference formulas?

a)

$\sin\left(\pi-\frac{11\pi}{12}\right)$

b)

$\sin(\pi)-\sin\left(\frac{11\pi}{12}\right)$

c)

$\sin\left(\frac{\pi}{3}-\frac{\pi}{4}\right)$

d)

$\sin\left(\frac{\pi}{3}\right)-\sin\left(\frac{\pi}{4}\right)$

7.

Expand $\sin\ \left(33^{o\ }+42^o\right)$

a)

$\sin\ 75^{o\ }$

b)

$\sin\ 33^o\cos42^o+\cos33^o\sin42^o$

c)

$\sin\ 33^o\cos42^o-\cos33^o\sin42^o$

d)

$\cos33^o\cos42^o+\sin33^o\sin42^o$

8.

Using the sum and difference formulas, condense into a single trig function: $\cos\left(46°\right)\cos\left(14°\right)+\sin\left(46°\right)\sin\left(14°\right)$

a)

cos(32°)

b)

cos(60°)

c)

sin(32°)

d)

sin(60°)

9.

Find the exact value of

\cos105\degree

a)

$\frac{\sqrt{2}+\sqrt{6}}{4}$

b)

$\frac{\sqrt{2}-\sqrt{3}}{2}$

c)

$\frac{\sqrt{6}-\sqrt{2}}{4}$

d)

$\frac{\sqrt{2}-\sqrt{6}}{4}$

10.

Which of the following is equivalent to $\tan\left(\alpha+\beta\right)$ ?

a)

$\frac{\tan\alpha+\tan\beta}{1-\tan\alpha\tan\beta}$

b)

$\frac{\tan\alpha-\tan\beta}{1-\tan\alpha\tan\beta}$

c)

$\frac{\tan\alpha+\tan\beta}{1+\tan\alpha\tan\beta}$

d)

$\frac{\tan\alpha-\tan\beta}{1+\tan\alpha\tan\beta}$

11.

Given tan α = 3/4 and tan β = (-1/2)

Please find the sum and difference:

tan (α-β)=

a)

$-\frac{10\sqrt{5}}{25}$

b)

$-\frac{2\sqrt{5}}{25}$

c)

$\frac{\sqrt{2}-\sqrt{6}}{4}$

d)

2

12.

Please select the correct solution

cos²x + sin ²x=

^{(It's on your reference sheet!!)}

a)

1

b)

csc²x + sec²x

c)

sin²x

d)

1 - sin²x

13.

$\tan105\degree$

a)

$2-\sqrt{3}$

b)

$2+\sqrt{3}$

c)

$-2-\sqrt{3}$

d)

$-2+\sqrt{3}$

Sum and Difference Formulas

Total questions: 13

Worksheet time: 45mins

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