In a triangle ABC, angle C= 90 degree,then findthe maximum value of sinA.sinB . Share with your friends Share 3 Vijay Kumar Gupta answered this It is required to find the maximum value of sinA·sinBNote that, sinA·sinB=12cosA-B-cosA+BThe sum of three angles in a triangle is 180°It is given that angle C=90° which implies that, A+B=180°-90°=90°Put this value in above to get, sinA·sinB=12cosA-B-cos90° =12cosA-B-0 =12cosA-BThe maximum value is when the given triangle is right isosceles triangle.That is the length of perpendicular and base are same.This further implies that the angles along the hypotenuse are equal. A=B (each 45° )So the maximum value of sinA·sinB is 12cos0°=121=12 13 View Full Answer
