# Regents Exam Questions A2.a.76: Angle Sum And Difference Identities 4 Worksheet With Answers

Regents Exam Questions A2.A.76: Angle Sum and Difference Identities 4 Name: _______________________
A2.A.76: Angle Sum and Difference Identities 4: Apply the angle sum and difference formulas
for trigonometric functions
1 If A and B are positive acute angles, sin A  5
8 If tan A  8 and tan B  1
,
, what is the value of
13
2
tan(A  B) ?
and cos B  4
, what is the value of sin(A  B) ?
5
9 If tan A  2
and tan B  1
, what is the value of
2 If sin x  12
, cos y  3
3
2
, and x and y are acute
13
5
tan(A  B) ?
angles, the value of cos(x  y) is
10 If tan A  2
5
and sin B 
and angles A and B
3 If sin A  3
, sin B  5
3
41
, and angles A and B are
5
13
are in Quadrant I, find the value of tan(A  B) .
acute angles, what is the value of cos(A  B) ?
11 If tan A  2
and tan B  3 , express tan(A  B) as a
4 If A and B are both acute angles, sin A  5
3
and
13
fraction in simplest form.
sin B  4
, then sin(A  B) is
5
12 When sin x   8
and x lies in Quadrant III and
17
5 If cos x  12
and sin y  4
, then sin(x  y) equals
cos y   4
and y lies in Quadrant II, what is
13
5
5
cos(x  y) ?
6 Given angle A in Quadrant I with sin A  12
and
13
13 Using the formula for cos(x  y) , find the exact
angle B in Quadrant II with cos B   3
, what is the
value of cos 15 in radical form if mx  45 and
5
my  30 .
value of cos(A  B) ?
14 Express as a single fraction the exact value of
7 If sin A  4
, tan B  5
, and angles A and B are in
sin 75 .
5
12
Quadrant I, what is the value of sin(A  B) ?
15 If sin x  4
, where 0  x  90 , find the value of
5
cos(x  180) .
1

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