# Trigonometry

If sin(A+B)=1 and cos(A-B)=1, then it means that sin(A+B) = cos(A-B).

Therefore, sin(A+B) = cos[90 -(A+B)] = cos(A-B)

Thus, 90-A-B = A-B

2A = 90

A = 45

Also, B = 45.

Substituting A = 45 in 4tanA-√2 secB-1/√2 cosecA, we get,

= 4tan(45)-√2 sec(45)-1/√2 cosec(45)

= 4 .1 – √2 . √2 – 1/√2 . √2

= 4 – 1 – 1

= 2.