Question

prove that cos 20 + sin 20 /cos 20-sin 20 =tan65

Answer 1

hey mate hope it Will help you
here formula was tan ( π\4+theta)= tan a + tan b/tan a -tanb

Answer 2

Answer:

Step-by-step explanation:

The given equation is:

$\frac{cos20+sin20}{cos20-sin20}=tan65$

Taking the left hand side of the above equation, we get

$\frac{cos20+sin20}{cos20-sin20}$

$\frac{cos20(1+\frac{sin20}{cos20})}{cos20(1-\frac{sin20}{cos20})}$

$\frac{1+tan20}{1-tan20}$

Now, we know that $tan45=1$, therefore the above equation becomes,

$\frac{tan45+tan20}{tan45-tan20}$

Using, $tan(A+B)=\frac{tanA+tanB}{1-tanAtanB}$, the above equation becomes,

$tan(45+20)$

$tan65$=RHS

Hence proved.