If A and B are complimentary angles, then : - Vidyadip

MCQ

If $A$ and $B$ are complimentary angles, then :

✓
$\left( {1\,\, + \,\,\tan \,\frac{A}{2}} \right)\,\,\left( {1\,\, + \,\,\tan \,\frac{B}{2}} \right) = 2$
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
$\left( {1\,\, - \,\,\tan \,\frac{A}{2}} \right)\,\,\left( {1\,\, - \,\,\tan \,\frac{B}{2}} \right) = 2$

✓

Answer

Correct option: A.

$\left( {1\,\, + \,\,\tan \,\frac{A}{2}} \right)\,\,\left( {1\,\, + \,\,\tan \,\frac{B}{2}} \right) = 2$

a
$A = \pi /2 - B \Rightarrow \frac{A}{2}$ $= \frac{\pi }{4} - \frac{B}{2}$

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

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