Question

tan theta under root 1 minus sin theta by under root 1 minus cos square theta​

Answer 1

Step-by-step explanation:

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Answer 2

We need to recall the following trigonometric formulas.

• $tan\theta=\frac{sin\theta}{cos\theta}$
• $sin^2\theta+cos^2\theta=1$
• $\frac{1}{cos\theta}=sec\theta$

Given:

$tan\theta(\sqrt{\frac{1-sin\theta}{1-cos^2\theta} } )$

$=tan\theta(\sqrt{\frac{1-sin\theta}{1-(1-sin^2\theta)} } )$

$=\frac{sin\theta}{cos\theta} (\sqrt{\frac{1-sin\theta}{sin^2\theta} } )$

$=\frac{sin\theta}{cos\theta} (\frac{1}{sin\theta} \sqrt{1-sin\theta} } )$

$=\frac{1}{cos\theta} (\sqrt{1-sin\theta} } )$

$=sec\theta(\sqrt{1-sin\theta} } )$