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cosec x-sinx=m , secx-cosx=n, eliminate x

cosec x-sinx=m , secx-cosx=n, eliminate x

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2 Answers

sidharth kriplani
35 Points
8 years ago

sqaure cosecx-sinx=m and secx-cosx=n and then add the resulting equations. open sec²x=tan²x+1 and cosec²x=cot²x+1. tan²x+cot²x=1 and sin²x+cos²x=1. the answer will be m²⁄n²= -1 or m²+n²=0

Lab Bhattacharjee
121 Points
5 years ago
m\sin x=\cos^2x \text{ and } n\cos x=\sin^2x=(\cos^2x/m)^2 \right )\implies\cos^3x=m^2n \\ \text{and similarly, }\sin^3x=mn^2 \\\text{Method}1:\\ \implies(m^2n)^{2/3}+ (mn^2)^{2/3}=1 \\\text{Method}2:\\ \sin^6x+\cos^6x=(\sin^2x)^3+(\cos^2x)^3=1-3\sin^2x\cos^2x \\ (m^2n)^2+(mn^2)^2=1-3(\sin^2x\cos^2x)\\ (1-\{(m^2n)^2+(mn^2)^2\})^3 = 3^3(mn^2\cdot m^2n)^2

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