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If tan x = \(\frac{4}{3}\), then the value of \(\sqrt{\frac{(1-sin\,x)(1+sin\,x)}{(1+cos\,x)(1-cos\,x)}}\) is

(a) \(\frac{9}{16}\) 

(b) \(\frac34\)

(c) \(\frac43\) 

(d) \(\frac{16}{9}\)

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(b) \(\frac34\)

 \(\sqrt{\frac{(1-sin\,x)(1+sin\,x)}{(1+cos\,x)(1-cos\,x)}}\) = \(\sqrt{\frac{1-sin^2\,x}{1-cos^2\,x}}\)      (∵ (a – b) (a+b) = a2 – b2)

\(\sqrt{\frac{cos^2\,x}{sin^2\,x}}\)                  (∵ sin2x + cos2x = 1)

\(\frac{cos\,x}{sin\,x}\) = cot θ = \(\frac{1}{tan\,\theta} = \frac{1}{\frac{4}{3}}=\frac34.\)

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