Answers and Explanations 171
Answers
101–200
125.
cosθ
Simply rewrite cotangent and simplify:
sin cot
sin cos
sin
cos
θ
θ
θ
θ
θ
θ
=
( )
=
126.
sin x tan x
Begin by writing sec x as 1
cos x
. Then get common denominators and simplify:
sec
cos
cos
cos
cos
cos
sin
cos
sin
sin
cos
x
x
x
x
x
x
x
x
x
x
x
−
=
−
= −
=
=
( )
1
1
1
2
2
= = sin tan
x
x
127.
1 + sin 2x
Expand the given expression and use the identity sin
2 
x + cos
2 
x = 1 along with
2 sin x cos x = sin(2x):
sin
cos
sin
cos
sin
cos
sin
c os sin
cos
x
x
x
x
x
x
x
x
x
x
+
(
)
=
+
(
)
+
(
)
=
+
+
=
2
2
2
2
1 1 2
1
2
+
= +
cos sin
sin
x
x
x
128.
sin x
Use the identity sin(A – B) = sin A cos B – cos A sin B on the expression
sin(π – x):
sin(
)
sin cos
cos sin
cos
( )sin
sin
π
π
π
−
=
−
=
− −
=
x
x
x
x
x
x
0
1