Question

tan80=a and tan 47 =b then tan 37 is equal to

Answer 1

Step-by-step explanation:

tan80= tan(90-10)= cot10

tan80=cot10

a = cot10

1/a = tan10

tan47 = tan (10+37)

$\tan(47) = \frac{ \tan(10) + \tan(37) }{1 - \tan(10) \tan(37) }$

$b = \frac{ \frac{1}{a} + \tan(37) }{1 - \frac{ \tan(37) }{a} }$

$b - \frac{b \tan(37) }{a} = \frac{1}{a} + \tan(37)$

$b - \frac{1}{a} = \tan(37) + \frac{b \tan(37) }{a}$

$\frac{ab - 1}{a} = \frac{a \tan(37) + b \tan(37) }{a}$

$ab - 1 = a \tan(37) + b \tan(37)$

$ab - 1 = \tan(37) \: (a + b)$

$\frac{ab - 1}{(a + b)} = \tan(37)$

Therefore, $\tan(37) = \frac{ab - 1}{(a + b)}$