Trigonometric Equations

Given,

a%5C%2C%20sin%5E%7B-1%7D%20%5C%2Cx%20-%20b%20%5C%2Ccos%5E%7B-1%7D%20%5C%2Cx%20%3D%20c%5C%2C%5C%2C%5C%2C...(i)

%5CRightarrow%20a%5Cleft(%5Cfrac%7B%5Cpi%7D%7B2%7D%20-%20cos%5E%7B-1%7Dx%5Cright)%20-%20b%5C%2C%20cos%5E%7B-1%7D%20x%3Dc

%5CRightarrow%20%5Cleft(a%20%2B%20b%5Cright)cos%5E%7B-1%7Dx%20%3D%20%5Cfrac%7Ba%5Cpi%7D%7B2%7D%20-%20c

%5CRightarrow%20cos%5E%7B-1%7D%20x%20%3D%20%5Cfrac%7Ba%5Cpi%20%2F2%20-c%7D%7Ba%2Bb%7D

Again from E

(i)

a%5C%2C%20sin%5E%7B-1%7D%20x%20-%20b%20(%5Cfrac%7B%5Cpi%7D%7B2%7D%20-%20sin%5E%7B-1%7D%20%5C%2Cx%20)%20%3D%20c

%5CRightarrow%20(sin%5E%7B-1%7D%20x)%20-%20(%20a%20%2B%20b%20)%20%3D%20c%20%2B%20%5Cfrac%7Bb%5Cpi%7D%7B2%7D

%5CRightarrow%20sin%5E%7B-1%7D%20x%20%3D%20%5Cfrac%7Bc%20%2B%20b%5Cpi%2F2%7D%7Ba%20%2B%20b%7D

%5Ctherefore%20a%5C%2C%20sin%5E%7B-1%7D%20%5C%2Cx%20%2B%20b%20%5C%2Ccos%5E%7B-1%7D%5C%2Cx%20%3D%20%5Cfrac%7Ba(c%20%2B%20b%5Cpi%2F2)%7D%7Ba%20%2B%20b%7D

%2B%20%5Cfrac%7Bb(a%5Cpi%2F2%20-%20c%20)%7D%7Ba%20%2B%20b%7D

%3D%20%5Cfrac%7Bc(a%20-%20b)%20%2B%20ab%5Cpi%7D%7Ba%20%2B%20b%7D

Chapter Questions
2 MCQs