Question

prove
$a = \sin(x) \: and \: b = \tan(x) \: then \: prove \: that \: \frac{1}{ {a}^{2} } - \frac{1}{ {b}^{2} } = 1$

Answer 1

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@Rajukumar111

Answer 2

Given,
a= sinx
b= tanx
.
Taking LHS,

→1/a² -1/b² putting a= sinx and b= tanx we get,

→1/sin²x -1/tan²x

→1/sin²x -cot²x ........(cotx = 1/tanx)

→1/sin²x - cos²x/sin²x

Taking LCM,

→(1 - sin²x)/cos²x

We know that sin²x + cos²x=1 or (1-sin²x) = cos²x

Hence,
(1 - sin²x)/cos²x

→cos²x/cos²x
→ 1 .

Proved.