Question

if sinA÷sinB=p and cosA÷cosB=q find tanA and tanB

Answer 1

Answer:

$Tan A = \frac{p}{q}Tan B$ and $\frac{q}{p}Tan A = Tan B$

Step-by-step explanation:

$Sin A \div Sin B = p$

$cos A \div cos B = q$

We are supposed to find tanA and tanB

We know that $Tan x = \frac{Sin x}{Cosx}$

Find the value of Sin A and Cos A

$Sin A= p \times Sin B$

$cos A = q \times Cos B$

$Tan A = \frac{Sin A}{Cos A}$

$Tan A = \frac{ p \times Sin B}{q \times Cos B}$

Using identity $\frac{Sin B}{Cos B}= Tan B$

So, $Tan A = \frac{p}{q}Tan B$

$\frac{q}{p}Tan A = Tan B$

So,  $Tan A = \frac{p}{q}Tan B$ and $\frac{q}{p}Tan A = Tan B$