Math, asked by JunglekiRani, 8 months ago

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

Answers

Answered by dhanikaR
3

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Answered by jitumahi435
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} } )

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