cot theta + tan theta = cosec theta sec theta
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Step-by-step explanation:
Answer and Explanation:
We are given:
cot
θ
+
tan
θ
=
sec
θ
csc
θ
Now simplify
cot
θ
+
tan
θ
Apply the trigonometric ratio
cot
θ
=
cos
θ
sin
θ
,
tan
θ
=
sin
θ
cos
θ
=
cos
θ
sin
θ
+
sin
θ
cos
θ
=
sin
2
θ
+
cos
2
θ
sin
θ
cos
θ
Apply the trigonometric identity
sin
2
θ
+
cos
2
θ
=
1
=
1
sin
θ
cos
θ
Next simplify
sec
θ
csc
θ
Apply the trigonometric ratio
sec
θ
=
1
cos
θ
,
csc
θ
=
1
sin
θ
=
1
cos
θ
⋅
1
sin
θ
=
1
sin
θ
cos
θ
Hence,
cot
θ
+
tan
θ
=
sec
θ
csc
θ
is proved.
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