Question

if cos A= 0.5 and cos b= 1/ √2
find the value of tan A- tan B ÷1+ tan A tan B

Answer 1

Answer:

2-\sqrt3

Step-by-step explanation:

the same formula for tan(B) tells us that $tan(B)=1$

so the final answer is: $\frac{\sqrt3-1}{1+(\sqrt3*1)} =\frac{\sqrt3-1}{\sqrt3+1}$

we need to rationalize the denominator: $\frac{\sqrt3-1}{\sqrt3+1} *\frac{\sqrt3-1}{\sqrt3-1} =\frac{3-2\sqrt3+1}{3-1} =\frac{4-2\sqrt3}{2} =\frac{2(2-\sqrt3)}{2} =2-\sqrt3$

sorry for disarrangement. read below formulas first

$1+tan^2(A)=\frac{1}{cos^2(A)} \\1+tan^2(A)=\frac{1}{(0.5)^2} \\1+tan^2(A)=4\\tan^2(A)=3\\tan(A)=\sqrt3$