Let tanx=a2−b22ab, where a<b<0 and 0<x<90. Draw a right triangle with angle x and label two sides of the triangle so that tanx=a2−b22ab. Now find sinx.
Solution
From the figure, sinx=c2ab. But what is c?
c2=(a2−b2)2+(2ab)2===a4−2a2b2+b4+4a2b2a4+2a2b2+b4(a2+b2)2.
Thus c=a2+b2, and sinx=a2+b22ab.