Question

Sin (a+b)/ cos (a-b) = 1-m/1+m , prove that tan (π/4-a) tan (π/4-b) = m .

Answer 1

sin (A+B) / cos (A-B) = (1-m)/(1+m)
sin(A+B) + m sin(A + B) = cos(A-B) - m cos(A-B)

m(sin A cos B + cos A sin B + cos A cos B + sin A sin B) =
cos A cos B + sin A sin B - sin A cos B - cos A sin B)

(sin A + cos A) (sin B + cos B)m = (sin A - cos A) (sin B - cos B)

m = ((sin A - cos A) / (sin A + cos A)) ((sin B - cos B) / (sin B + cos B))

m = ((tan A - 1) / (1 + tan A)) (tan B - 1) / (1 + tan B))

m = ((1 - tan A) / (1 + tan A)) (1 - tan B) / (1 + tan B))

m = tan (π/4 - A) tan (π/4 - B)






Hope it helps! :)
Mark brainliest if it did!