trigo eqn

value of a for which the equation
4cosec²[pi(a+x)]+a²-4a=0
has real roots.....

2 Answers

341

Hari Shankar ·2011-08-07 02:05:15

\because \csc^2 \theta \ge 1 we have

LHS = 4 \csc^2 (\pi(a+x)) + a^2-4a \ge a^2-4a+4 = (a-2)^2 \ge 0

Equality occurs when a =2 and \pi (2+x) = (2k+1)\frac{\pi}{2}

or x = k -\frac{3}{2} for some integer k

thank you sir

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