If cos A=1/2 and sin B= 1/root 2 , find the value of:

tan a-tan b / 1+tanA. tan B

Question

If cos A=1/2 and sin B= 1/root 2 , find the value of:
tan a-tan b / 1+tanA tan B

Shridhar Kaushik · Accepted Answer

$Given: cos A = \frac{1}{2} \Rightarrow A = 60 ° \Rightarrow \tan A = \tan 60 ° = \sqrt{3} and sin B = \frac{1}{\sqrt{2}} \Rightarrow B = 45 ° \Rightarrow \tan B = \tan 45 ° = 1$

So,

$\frac{\tan A - \tan B}{1 + \tan A \tan B} = \frac{\sqrt{3} - 1}{1 + \sqrt{3} \times 1} = \frac{\sqrt{3} - 1}{\sqrt{3} + 1} = \frac{(\sqrt{3} - 1) (\sqrt{3} - 1)}{(\sqrt{3} + 1) (\sqrt{3} - 1)} = \frac{3 + 1 - 2 \sqrt{3}}{3 - 1} = \frac{4 - 2 \sqrt{3}}{2} = 2 - \sqrt{3}$

If cos A=1/2 and sin B= 1/root 2 , find the value of: tan a-tan b / 1+tanA. tan B

If cos A=1/2 and sin B= 1/root 2 , find the value of:

tan a-tan b / 1+tanA. tan B