Question

If sin A= root3/2 & cos B= root3/2, find the value of: tan A - tan B/1+tan A tan B.

Answer 1

sin a=root3/2 hence   a=60 degree
cosb =root3/2   b=30 degree
as we knw 
(tanA-tanB)/1+tanAtanB= tan(A-B)  where A=60 degree and b= 30 degree 
hence tan(60-30)=tan30= 1/root 3   

Answer 2

[tex] \ Sin\ A\ = \frac{\sqrt{3}}{2} \ \ \ Cos\ A = \sqrt{1 - \frac{3}{2^2}} = \frac{1}{2} \\ \\ Cos\ B = \frac{\sqrt{3}}{2} \ \ \ \ \ Sin\ B = \sqrt{1 - \frac{3}{2^2}} = \frac{1}{2} \\ \\ Tan\ A = \sqrt{3} \ \ \ Tan B\ = \frac{1}{\sqrt{3}} \\ \\ Value\ = \ \frac{{\sqrt{3}} - \frac{1}{\sqrt{3}}}{1 + \sqrt{3} * \frac{1}{\sqrt{3}}} = \frac{\frac{3 - 1}{\sqrt{3}}}{2} = \frac{1}{\sqrt{3}} \\ \\ [/tex]

Actually, it can be done also, as Sin (A-B) / cos (A-B)

Also, A= 60 deg, B = 30 deg
Tan (a-B) = tan 30 deg = 1/√3

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