** sine = a cos aihe cos 0 = b sino...
Question

# ** sine = a cos aihe cos 0 = b sino, -1) cor*(1-b) coto find

Railway Exams
Maths
Solution
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( sin theta=a cos phi ) ( cos theta=operatorname{la} sin phi ) ( =left(a^{2}-1right) cot ^{2} phi+left(1-b^{2} cot ^{2} thetaright. ) ( =left(a^{2}-1right) frac{cos ^{2} phi}{sin ^{2} phi}+left(1-b^{2}right) frac{cos ^{2} theta}{sin ^{2} theta} ) ( =frac{a^{2} cos ^{2} phi-cos ^{2} phi}{sin ^{2} phi}+frac{cos ^{2} theta-b^{2} cos ^{2} theta}{sin ^{2} theta} ) ( Rightarrow quad sin theta=a cos phi ) ( sin ^{2} theta=a^{2} cos ^{2} phi ) ( cos ^{2} phi=frac{sin ^{2} theta}{a^{2}} ) ( b sin phi=cos theta ) ( b^{2} sin ^{2} phi=cos ^{2} theta ) ( sin ^{2} alpha=frac{cos ^{2} theta}{b^{2}} ) ( sin frac{cos ^{2} phi}{sin ^{2} phi}=frac{sin ^{2} theta}{a^{2} cos ^{2} theta}=frac{b^{2}}{a^{2}} tan ^{2} theta ) ( sin left(a^{2}-1right) frac{b^{2}}{a^{2}} tan ^{2} theta+left(1-b^{2}right) cot ^{2} theta ) ( =b^{2} tan ^{2} theta-frac{b^{2}}{a^{2}} tan ^{2} theta+cot ^{2} theta-b^{2} cot ^{2} theta ) Answer is ginderendent of ( theta ), soput ( theta=45^{circ} ) ( =b^{2}-frac{b^{2}}{a^{2}}+1-b^{2}=frac{a^{2}-b^{2}}{a^{2}} sin s(3) )