Question

$9A\sqrt{\frac{co{s}^{7}x}{si{n}^{11}x}}+5B\sqrt{\frac{co{s}^{3}x}{si{n}^{7}x}}=\sqrt{\frac{co{s}^{3}x}{si{n}^{11}x}}$,find A and B

Answer 1

$\begin{array}{c}9A\sqrt{\frac{{\cos }^{7}x}{{\sin }^{11}x}}+5B\sqrt{\frac{{\cos }^{5}x}{{\sin }^{7}x}}=\sqrt{\frac{{\cos }^{3}x}{{\sin }^{11}x}}\\ dividewholeequationby\sqrt{\frac{{\cos }^{3}x}{{\sin }^{11}x}}\\ weget\\ 9A{\cos }^{2}x+5B{\sin }^{2}x=1\\ fromhere9A=1and5B=1\\ So,A=1/9andB=1/5.Ans.\end{array}$