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3.Trigonometrical Ratios, Functions and Identities
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જો $A$ અને $B$ એ કોટિકોણ હોય તો નીચેનામાંથી ક્યું સાચું છે ?
A
$\left( {1\,\, + \,\,\tan \,\frac{A}{2}} \right)\,\,\left( {1\,\, + \,\,\tan \,\frac{B}{2}} \right) = 2$
B
$\left( {1\,\, + \,\,\cot \,\frac{A}{2}} \right)\,\,\left( {1\,\, + \,\,\cot \,\frac{B}{2}} \right) = 2$
C
$\left( {1\,\, + \,\,\sec \,\frac{A}{2}} \right)\,\,\left( {1\,\, + \,\,\cos ec\,\frac{B}{2}} \right) = 2$
D
$\left( {1\,\, - \,\,\tan \,\frac{A}{2}} \right)\,\,\left( {1\,\, - \,\,\tan \,\frac{B}{2}} \right) = 2$
Solution
$A = \pi /2 – B \Rightarrow \frac{A}{2}$ $= \frac{\pi }{4} – \frac{B}{2}$
Hence $1 + tanA/2 = 1 + \frac{{1 – \tan \,B/2}}{{1 + \tan \,B/2}}$ $= \frac{2}{{1 + \tan \,\frac{B}{2}}}$
Hence $A$ is correct
Standard 11
Mathematics
