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If a belongs to (π/2, π), then [√(x 2 +x)] + [(tan 2 a)/√(x 2 +x)] is always greater than or equal to (A) 2tan a (B) 1 (C) -1 (D) -2tan a

If a belongs to (π/2, π), then [√(x2+x)] + [(tan2a)/√(x2+x)] is always greater than or equal to
 
(A) 2tan a
(B) 1
(C) -1
(D) -2tan a

Grade:11

1 Answers

jagdish singh singh
173 Points
5 years ago
\hspace{-0.75 cm}\displaystyle f(x)=\sqrt{x^2+x}+\frac{\tan^2\alpha}{\sqrt{x^2+x}}$\\\\\\ $\displaystyle f(x) =\bigg[\sqrt{\sqrt{x^2+x}}-\frac{\tan\alpha}{\sqrt{\sqrt{x^2+x}}}\bigg]^2+2\cdot \sqrt{\sqrt{x^2+x}}\cdot \frac{\tan\alpha}{\sqrt{\sqrt{x^2+x}}}\geq 2\tan\alpha...............................................
 
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