Verify the given trigonometric equation — task. Mathematics State Board, Class 10.

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Answer variants:

$\sqrt{\frac{{(1 + \sin θ)}^{2}}{1 - \sin^{2} θ}}$

$\frac{1 + \sin θ}{\cos θ}$

$\sqrt{\frac{{(1 + \sin θ)}^{2}}{\cos^{2} θ}}$

$\sqrt{\frac{{(1 + \sin θ)}^{2}}{1 + \sin^{2} θ}}$

$\frac{1}{\cos θ} + \frac{\sin θ}{\cos θ}$

$\sqrt{\frac{1 + \sin θ}{1 - \sin θ} \times \frac{1 + \sin θ}{1 + \sin θ}}$

$\sqrt{\frac{1 + \sin θ}{1 - \sin θ} \times \frac{1 - \sin θ}{1 - \sin θ}}$

Verify that

$\sqrt{\frac{1 + \sin θ}{1 - \sin θ}}$

$=$

$\sec θ + \tan θ$ .

Proof:

LHS

$=$

$\sqrt{\frac{1 + \sin θ}{1 - \sin θ}}$

$=$

$\sec θ + \tan θ$

$=$ RHS

Did you find an error?

10. Verify the given trigonometric equation