Question

sinA=cos30° valculateA

Answer 1

cos (a-b) = cosa*cos b + sin b*sin a 

cos (a+b) = cosa*cos b - sin b*sin a 

We'll put a = 30 and b = A. 

cos (30+A) = cos 30*cos A - sin A*sin 30 

cos (30-A) = cos 30*cos A + sin A*sin30 

Now, we'll replace these in the original equation: 

cos (30-A) - cos (30+A) 

= cos 30*cos A + sin A*sin30 - (cos 30*cos A - sin A*sin 30) 

= cos 30*cos A + sin A*sin30 - cos 30*cos A + sin A*sin 30 

the cos30*cosA is subtracted so we are left with 2sinAsin30 

sin 30 = 1/2, so 2sinAsin30 = 2sinA*(1/2) = sinA as 2*(1/2) = 1

Answer 2

sinA = cos 30°
sinA = √3/2
sinA = sin 60°
so, A = 60°