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A sin^2tha+bcos^2tha=c then prove that tan tha=sqrt c-b/a-c

Answer»

asin^2(x) +bcos^2(x) = c \\asin^2(x) +b(1 - sin^2(x)) = c\\sin^2(x) = \frac{c-b}{a-b} \\cos^2(x) = 1- \frac{c-b}{a-b} = \frac{a-c}{a-b} \\tan^2(x) = \frac{sin^2(x)}{cos^2(x)} \\ = \frac{(c-b)/(a-b)}{(a-c)/(a-b)} \\= \frac{c-b}{a-c} \\Hence, tan(x) = \sqrt{\frac{c-b}{a-c} }


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