Question

If Sin ( A+B) = 1 , Cos ( A-B)=1,0<A+ B<90, A>= B, Find A and B​

Answer 1

Given that,

sin(A + B) = 1

$\longrightarrow$ sin(A + B) = sin(90)

$\longrightarrow$ A + B = 90 -------(1)

Also,

cos(A - B) = 1

$\longrightarrow$ cos(A - B) = cos0

$\longrightarrow$ A - B = 0 --------(2)

Adding equations (1) and (2),

A + B + A - B = 90

$\longrightarrow$ 2A = 90

$\longrightarrow$ A = 45°

Putting value of A in (1),

A + B = 90

$\longrightarrow$ B = 90 - 45°

$\longrightarrow$ B = 45°

Thus, A = B = 45°.

Answer 2

Given that,

sin(A + B) = 1

⟶ sin(A + B) = sin(90)

⟶ A + B = 90 -------(1)

Also,

cos(A - B) = 1

⟶ cos(A - B) = cos0

⟶ A - B = 0 --------(2)

Adding equations (1) and (2),

A + B + A - B = 90

⟶ 2A = 90

⟶ A = 45°

Putting value of A in (1),

A + B = 90

⟶ B = 90 - 45°

⟶ B = 45°

Thus, A = B = 45°.