CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon


Question

If $$\displaystyle \sin A+\cos 2A=1/2$$ and $$\displaystyle \cos A+\sin 2A=1/3,$$ then find the value of $$\sin 3A$$


Solution

Given, $$\displaystyle \sin  A+\cos  2A=\frac { 1 }{ 2 } ,\cos  A+\sin  2A=\frac { 1 }{ 3 } $$
Squaring and adding 
$$\sin ^{ 2 }{ A } +\sin ^{ 2 }{ 2A } +2\sin { A } \cos { 2A } +\cos ^{ 2 }{ A } +\cos ^{ 2 }{ 2A } +2\cos { A } \sin { 2A } =\frac { 1 }{ 4 } +\frac { 1 }{ 9 } $$
$$\displaystyle \Rightarrow 2+2\sin { 3A=\frac { 13 }{3 6 } \Rightarrow \sin { 3A } =\frac { -59 }{ 72 }  } $$

Mathematics

Suggest Corrections
thumbs-up
 
0


similar_icon
Similar questions
View More


similar_icon
People also searched for
View More



footer-image