Question

if in a triangle abc angle c is 90 then maximum value of sinasinb

Answer 1

Answer:

Step-by-step explanation:

sinAsinB is maximum    when A =B =45

sinAsinB  = sin45sin45  = [1/√2][1/√2] = 1/2

Answer 2

Maximum value of sinasinb = 1/2 if in a triangle abc angle c is 90°

Given:

Triangle abc

angle c = 90°

To Find:

maximum value of sinasinb

Solution:

Sum of angles if a triangle is 180°

a + b + c = 180°

Substitute c = 90°

a + b + 90° = 180°

a+ b = 90°

=> b = 90° - a

sinasinb

substitute b = 90° - a

= sinasin(90° - a)

use sin (90° - x ) = cosx

= sinacosa

Using sin2a = 2sinacosa

= sin2a/2

Maximum value of sin 2a = 1  as sin function varies from -1 to 1

= 1/2

Hence, maximum value of sinasinb = 1/2 if in a triangle abc angle c is 90°