Question

Tan theta =4/3 show that root 1-sin theta/1+sin theta

Answer 1

$\textbf{Given:}$

$tan\theta=\dfrac{4}{3}$

$\textbf{To find:}$

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

$\text{Consider,}$

$tan\theta=\dfrac{4}{3}$

$\text{Taking reciprocals, we get}$

$cot\theta=\dfrac{3}{4}$

$\text{We know that}$

$\boxed{\bf\;cosec^2A=1+cot^2A}$

$cosec^2\theta=1+cot^2\theta$

$cosec^2\theta=1+\dfrac{9}{16}$

$cosec^2\theta=\dfrac{25}{16}$

$cosec\theta=\dfrac{5}{4}$

$\implies\bf\,sin\theta=\dfrac{4}{5}$

$\text{Now,}$

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

$=\sqrt{\dfrac{1-\dfrac{4}{5}}{1+\dfrac{4}{5}}}$

$=\sqrt{\dfrac{\dfrac{1}{5}}{\dfrac{9}{5}}}$

$=\sqrt{\dfrac{1}{9}}$

$=\dfrac{1}{3}$

$\therefore\bf\sqrt{\dfrac{1-sin\theta}{1+sin\theta}}=\dfrac{1}{3}$

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Answer 2

plz take help of the attachment i have given