Given-cos-x-sin-x-p-sec-x-csc-x-q-p-q-Find-cos-2-x-2-2sin-2-x-csc-2-x-

Question Number 126610 by bramlexs22 last updated on 22/Dec/20

G i v e n {\begin{cases} \cos x + \sin x = p \\ \sec x + \csc x = q \end{cases}

p \neq q . F i n d \frac{\cos^{2} x}{2 - 2 \sin^{2} x - cs c^{2} x} .

Answered by liberty last updated on 22/Dec/20

q = (\frac{\cos x + \sin x}{\cos x \sin x}) \Rightarrow q^{2} = \frac{p^{2}}{\cos^{2} x \sin^{2} x}

\cos^{2} x \sin^{2} x = \frac{p^{2}}{q^{2}} \dots (i)

\Rightarrow \frac{\cos^{2} x}{2 \cos^{2} x - \frac{1}{\sin^{2} x}} = \frac{\cos^{2} x \sin^{2} x}{2 \cos^{2} x \sin^{2} x - 1}

= \frac{(\frac{p^{2}}{q^{2}})}{(\frac{2 p^{2}}{q^{2}} - 1)} = \frac{p^{2}}{2 p^{2} - q^{2}}

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