Question

SinA.CosA= 1/2 then find the value of A

Answer 1

Answer:

that the question was wrong that must be

find the value os sina+cosb

Step-by-step explanation:

sin(a) + cos(a) = 1/2 … (1) implies sin(a) + sqrt[1 - sin^2(a)] = 1/2 or:

2sqrt[1 - sin^2(a)] = 1 - 2sin(a) square both sides, you get:

4[1 - sin^2(a)] = 1 - 4sin(a) + 4sin^2(a) or 8sin^2(a) - 4sin(a) -3 = 0

Use the quadratic form (Ax^2 + Bx + C = 0) to find sin(a):

A = 8, B = -4, and C = -3, therefore: sin(a) = [4 (+/-)sqrt(16 + 96)]/16 So: Either: sin(a) = [1 + sqrt(7)]/4 or sin(a) = [1 - sqrt(7)]/4 From (1), you get cos(a) = 1/2 - sin(a), therefore:

sin(a) X cos(a) = [1 + sqrt(7)]/4 X { 1/2 - [1 + sqrt(7)]/4} = -3/8, …. or:

sin(a) X cos(a) = [1 - sqrt(7)]/4 X { 1/2 - [1 - sqrt(7)]/4} = -3/8

Answer 2

Answer:

45°

Step-by-step explanation:

sinAcosA = 1/2

=> 2sinA cosA= 1

=> sin 2A= 1

=> 2A= sin inverse(1)

=> 2A= 90°

=> A= 45°