costheta/1-sintheta + costheta/1+sintheta=sectheta
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Step-by-step explanation:
The LHS of the proving statement is given as
cos
θ
1
−
sin
θ
Multiply and divide by
(
1
+
sin
θ
)
=
cos
θ
(
1
+
sin
θ
)
(
1
−
sin
θ
)
(
1
+
sin
θ
)
=
cos
θ
+
cos
θ
sin
θ
1
−
sin
2
θ
By the identity,
sin
2
θ
+
cos
2
θ
=
1
,
=
cos
θ
+
cos
θ
sin
θ
cos
2
θ
=
cos
θ
(
cos
θ
)
2
1
+
cos
θ
sin
θ
(
cos
θ
)
2
1
=
1
cos
θ
+
sin
θ
cos
θ
=
sec
θ
+
tan
θ
Hence proved!
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