Answer:
Explanation:
The reciprocal identities
csc
θ
=
1
sin
θ
sec
θ
=
1
cos
θ
cot
θ
=
1
tan
θ
The quotient identities:
tan
θ
=
sin
θ
cos
θ
cot
θ
=
cos
θ
sin
θ
Applying all these identities, on both sides, we get:
1
sin
x
+
1
cos
x
sin
x
+
cos
x
=
cos
x
sin
x
+
sin
x
cos
x
cos
x
+
sin
x
cos
x
sin
x
sin
x
+
cos
x
=
cos
x
sin
x
+
sin
x
cos
x
1
sin
x
+
cos
x
×
cos
x
+
sin
x
cos
x
sin
x
=
cos
x
sin
x
+
sin
x
cos
x
1
cos
x
sin
x
=
cos
2
x
+
sin
2
x
sin
x
cos
x
Applying the pythagorean identity
sin
2
x
+
cos
2
x
=
1
on the right side, we get:
1
cos
x
sin
x
=
1
sin
x
cos
x
Hopefully this helps!