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Question and Answer

\( (1+ta{n}^{2}\theta \left)\right(1+sin\theta \left)\right(1-sin\theta )=\)
(A) 2
(B) 3
(C) 1
(D) 4

Answer

(C)
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Solution

\( (1+ta{n}^{2}\theta \left)\right(1+sin\theta \left)\right(1-sin\theta )\)
\( \left(1+ta{n}^{2}\theta \right)(1-sin\theta +sin\theta -si{n}^{2}\theta )\)
\( (1+ta{n}^{2}\theta \left)\right(1-si{n}^{2}\theta )\)
\( \therefore\;1+ta{n}^{2}\theta =se{c}^{2}\theta ,si{n}^{2}\theta +co{s}^{2}\theta =1)\)
\( =(se{c}^{2}\theta \left)\right(co{s}^{2}\theta )\)
\( =se{c}^{2}\theta .\frac{1}{se{c}^{2}\theta }=1\)
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