If-x-0-pi-2-and-2cos-x-sin-x-cos-x-tan-2-x-lt-sec-2-x-has-solution-set-is-a-lt-x-lt-b-find-the-value-of-a-b-

Question Number 115348 by bemath last updated on 25/Sep/20

I f x \in (0, \frac{π}{2}) a n d 2 \cos x (\sin x + \cos x) + \tan^{2} x < \sec^{2} x

h a s s o l u t i o n s e t i s a < x < b . f i n d t h e

v a l u e o f a + b

Answered by bobhans last updated on 25/Sep/20

\Rightarrow \sin 2 x + 2 \cos^{2} x + \tan^{2} x < 1 + \tan^{2} x

\Rightarrow \sin 2 x + 2 (\frac{1}{2} + \frac{1}{2} \cos 2 x) < 1

\Rightarrow \sin 2 x + \cos 2 x < 0

w e g e t \frac{3 π}{8} < x < \frac{4 π}{8} \to t h e n a + b = \frac{7 π}{8}

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