If tan(-x), tan , tan (a + x) in or...
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If tan(-x), tan , tan (a + x) in order are three consecutive terms of a G.P. then sum of all the solutions in 0, 394 is ks. Find the value of a all the solutions in [0, 314) is kr. Find the value of k.

JEE/Engineering Exams
Maths
Solution
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( =tan ^{2} frac{pi}{12}=tan left(frac{pi}{2}-xright) tan left(frac{pi}{2}+xright) ) ( =(2-53)^{2}=sin left(frac{pi-w}{2}right)^{sin left(frac{pi}{12}+xright)}{left.cos left(frac{pi}{12}right)right) cos left(frac{pi}{12}+xright)} ) ( Rightarrow 7-453=frac{sin ^{2} frac{pi}{12}-sin ^{2} x}{cos ^{2} frac{pi}{12}-sin ^{2} x} ) ( begin{aligned} Rightarrow 7-453=& frac{4-2 sqrt{3}-sin ^{2} x}{8} frac{4+2 sqrt{3}}{8}-sin ^{2} x end{aligned} ) ( Rightarrow quad 7-453=frac{2-sqrt{3}-4 sin ^{2} x}{2+sqrt{3} cdot 9-4 sin ^{2} n} )
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