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Question and Answer

If \( cos\theta =\frac{1}{2}\) , the value of \( \frac{2sec\theta }{1+ta{n}^{2}\theta }\) is
(A) 2
(B) 0
(C) 1
(D) 3

Answer

(C)
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Solution

Here, \( cos\theta =\frac{1}{2}\)
\( B{C}^{2}=4-1\)
\( BC=\sqrt{3}\)
\( \therefore  \frac{2sec\theta }{1+ta{n}^{2}\theta }=\frac{2\times\;2}{1+(\sqrt{3}{)}^{2}}=\frac{4}{1+3}=\frac{4}{4}=1\)
\( \therefore  \left(sec\theta =\frac{2}{1},tan\theta =\frac{\sqrt{3}}{1}\right)\)
Solution for If  costheta =frac{1}{2} , the value of  frac{2sectheta }{1+ta{n}^{2}theta } is (A) 2(B) 0(C) 1(D) 3
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