[" 3.If "Sin A=cos B," then prove that "A+B=90^(@)],[" II.Answer the following anestions "]

If sin A-cos B=0, prove that A+B=90^(@)

If sin2A+sin2B=sin2C , prove that A=90^(@)" or " B=90^(@) .

Statement: If sin A =sin B, cos A=cos B then A=2n pi +B Statement :II If A+B+C=90^(@) then sin 2A+sin 2B+sin 2C=sin A sin B sin C Which of the above statement is correct?

If triangle ABC has AB = BC and /_B = 90^@ . Find the values of the following: (i) sin A (ii) cos A

If A and B are acute angles such that sin A =cos B , prove that (A+B)=90^@ .

Prove that : sin(A- B) = sin A cos B -cos A sin B .

If A +B = 90 , prove that (cos A + cos B)/(sin A+ sinB)=1 .

If A +B = 90 , prove that cos A = sqrt (cos A/sin B - sin A cos B) .

If A +B = 90 , prove that (sin A- sin B)^2 = 1-2 sin A cos A .

For any A,B in R, prove that cos(A-B)=cos A cos B+sin A sin B