If x sin theta simplify frac x sqrt 1 - x 2 - SS3 Mathematics Trigonometric Identities and Equations Question
If \(x = \sin\theta\), simplify \(\frac{x}{\sqrt{1 - x^{2}}}\)
A
\(\cos^{2}\theta\)
B
\(\tan\theta\)
C
\(\sin\frac{\theta}{2}\)
D
\(\tan^{2}\theta\)
correct option: b
\(\frac{x}{\sqrt{1 - x^{2}}} = \ \frac{\sin\theta}{\sqrt{1 - {(\sin x)}^{2}}} = \frac{\sin\theta}{\sqrt{1 - \sin^{2}\theta}} = \frac{\sin\theta}{\sqrt{\cos^{2}\theta}} = \frac{\sin\theta}{\cos\theta} = \tan\theta\)
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