If a cos 0 - b sin 0 = c, prove tha...
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If a cos 0 - b sin 0 = c, prove that a sin 0 + b cos 0 = Va? + b2 -ca,

11th - 12th Class
Maths
Solution
131
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( a cos theta-b sin theta=c ) Squaring both sides ( a^{2} cos ^{2} theta+b^{2} sin ^{2} theta-2 a b sin theta cos theta ) ( =c^{2} ) ( a^{2}left(1-sin ^{2} thetaright)+b^{2}left(1-cos ^{2} thetaright)-2 a b sin theta ) ( a^{2}-a^{2} sin ^{2} theta+b^{2}-b^{2} cos ^{2} theta-2 a b sin theta ) ( cos theta=c^{2} ) ( frac{7}{a} sin ^{2} theta+b^{2} cos ^{2} theta+2 a b sin theta cos ^{2}={ }^{2}=b^{2}-c^{2} ) ( (a sin theta+b cos theta)^{2}=a^{2}+b^{2}-c^{2} ) ( Rightarrow a sin theta+b cos theta=sqrt{a^{2}+b^{2}-c^{2}} )
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