If sin (A + B) = 1 and cos (A – B) = 1, 0°

Question

If sin (A + B) = 1 and cos (A &ndash; B) = 1, 0&deg; < A + B &le;90&deg;, A &ge; B find A and B.

Philoid · Accepted Answer

Given: sin (A + B) = 1 and cos (A – B) = 1

sin(A+B) = 1

Also, we know, sin 90⁰ = 1

$\Rightarrow$ sin(A+B) = sin 90⁰

or (A+B) = 90⁰ .............(1)

Now, cos (A – B) = 1

And, we know, cos 0⁰ = 1

$\Rightarrow$ (A - B) = 0⁰ .............(2)

On solving both equations (1) and (2) , we get

2A = 90⁰

or A = 90⁰/2

or A = 45°

Similarly, B = 45°