If-6tan-2-x-tan-x-sec-x-sec-2-x-where-pi-2-lt-x-lt-3pi-2-has-the-roots-x-1-and-x-2-Find-the-value-of-sin-x-1-x-2-

Question Number 128645 by john_santu last updated on 09/Jan/21

If 6 \tan^{2} x + \tan x . \sec x = \sec^{2} x where

\frac{π}{2} < x < \frac{3 π}{2} has the roots x_{1} and x_{2} . Find

the value of \sin (x_{1} + x_{2}) .

Answered by liberty last updated on 09/Jan/21

(∙) \frac{6 \sin^{2} x}{\cos^{2} x} + \frac{\sin x}{\cos^{2} x} = \frac{1}{\cos^{2} x}

(∙) 6 \sin^{2} x + \sin x - 1 = 0

(∙) (3 \sin x - 1) (2 \sin x + 1) = 0

(∵) {\begin{cases} \sin x_{1} = \frac{1}{3} \land \sin x_{2} = - \frac{1}{2} or \\ \sin x_{1} = - \frac{1}{2} \land \sin x_{2} = \frac{1}{3} \end{cases}

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