URGENT.......

If cosec (A+B) =1 and sec(A-B)=2, evaluate:

i). Sin A cos B + cos A sinB

ii). tan A + tan B

----------------------

1-tanA * tanB

Cosec(A+B) = 1 = Cosec 90

Therefore A +B = 90 ----- (1)

Again, Sec(A-B) = 2 = Sec 60

Therefore A-B = 60 ------- (2)

Adding (1) and (2)

A + B + A - B = 90 + 60

2A = 150

A = 75

Substituting A = 75 into equation (1)

75 + B = 90

B = 15

i) SinAcosB + SinBcosA

Substituting values of A and B in the above expression

Sin75 cos15 + sin15 Cos 75

cos (90 - 75) cos15 + sin 15 sin(90 - 75)

Cos 15 Cos 15 + sin 15 Sin 15

Cos² 15 + sin² 15 = 1

ii) The denominator is 1 - tanA tan B

Substituting the values of A and B in the above expression

1 - tan75 tan15

1- cot (90 - 75) tan 15

1- cot15 tan 15

1 - 1 -----( Because cot A * Tan A = 1)

0

Therefore since the denominator is 0, the divison of any no. by 0 is infinity.

Therefore, The answer is INFINITY.