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10.3 Worksheet
I. Simplify the given expressions using the appropriate
formulas. If possible, evaluate to find the exact value.
2)
3) cos2 5x  sin 2 5x
4) 6sin25°cos25°




5) 1-2sin220°
6) 3-6sin215°
8) 6cos2
7) 5sin10°cos10°
3
8
9)
2 3
1 tan
8
2tan
11)




4 tan 
1 tan 2 B


1) 2sin cos
2
2
2tan 65
1 tan 2 65
13)
1  cos4 x
2
15)
1  cos40
2
2
10)
 4  8sin


12
3

4
12) 2sin
5
5
cos
12
12
1 cos8x
14)
 1  cos8x

16)
1 cos210
sin 210
II. Use the half-angle formulas to determine the exact

values of the sine, cosine and tangent
of the angle.
a) 165
b) 3π/8
III. Find the exact values of sin(u/2), cos(u/2) , and
tan(u/2) using the half-angle formulas if:
secu = -7/2,
π/2 < u < π
IV. Find the exact values of sin2, cos2, and tan2.
a) sin=3/5
0 <  < π/2
b) cos= -2/3
π/2 <  < π
c) cot= -4
3π/2 <  < 2π
V. Answer the following questions.
3
a) Solve tan(Cos1( ))
5
b) Write the trigonometric expression as an algebraic
expression:
cos(2arccosx)

VI. Verify the following identities:
a) 1  cot 2 x (1 cos2x)  2
b)


1 cos2A
 tan 2 A
1  cos2A