Proof that sin2a cos2 a 10 Proof that for any triangle the

Proof that sin^2a + cos^2 a = 1.0 Proof that for any triangle, the following ratios are equal (the sin law). AB/Sin(c) = AC/Sin(b) = BC/Sin(a)

Solution

Sin²a + cos²a=1

Suppose we have a right triangle having adjacent=a,opposite=o and hypotenuse=h

And according to pythagoras theorem

h²=a²+o²

sin a=opposie/hypotenuse=o/h

Sin²a=o²/h²

Cos a=adjacent/hypotenuse=a/h

Cos²a= a²/h²

sin²a + cos²a = o²/h²   + a²/h² =(o²+a²)/h²

(o²+a²)/(o²+a²) =1