152 If tan 0 + sec 0 = x, show that sin 0=
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Answer:
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Step-by-step explanation:
Given
tan
θ
+
sec
θ
=
x
...
.
.
[
1
]
⇒
1
sec
θ
+
tan
θ
=
1
x
⇒
sec
θ
−
tan
θ
sec
2
θ
−
tan
2
θ
=
1
x
⇒
sec
θ
−
tan
θ
=
1
x
...
.
[
2
]
Adding [1] and [2] we get
2
sec
θ
=
x
+
1
x
...
.
[
3
]
Subtracting [2] from [1] we get
2
tan
θ
=
x
−
1
x
...
.
[
4
]
Dividing [4] by [3] we get
tan
θ
sec
θ
=
x
−
1
x
x
+
1
x
⇒
sin
θ
=
x
2
−
1
x
2
+
1
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