Question

prove that root of 1+sin theta / 1-sin theta + root of 1-sin theta / 1+sin theta = 2 sec theta

Answer 1

Answer:

$\sqrt{\frac{1+sin\theta}{1-sin\theta}}+\sqrt{\frac{1-sin\theta}{1+sin\theta}}=2sec\theta$

Step-by-step explanation:

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

=$\frac{\left(\sqrt{1+sin\theta}\right)^{2}+\left(\sqrt{1-sin\theta}\right)^{2}}{\sqrt{(1-sin\theta)(1+sin\theta)}}$

=$\frac{1-sin\theta+1+sin\theta}{\sqrt{1^{2}-sin^{2}\theta}}$

=$\frac{2}{\sqrt{cos^{2}\theta}}$

= $\frac{2}{cos\theta}$

= $2sec\theta$

=$RHS$

Therefore,

$\sqrt{\frac{1+sin\theta}{1-sin\theta}}+\sqrt{\frac{1-sin\theta}{1+sin\theta}}=2sec\theta$

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Answer 2

Answer:

please mark brainlist one time because I have done in full explanation