Question

if tan a=5/6 and tanb=1/11 show that a+b=π/4

— No spam! ​

Answer 1

tan(a+b)

= (tan a + tan b) / (1 – tan a.tan b)

= ( 5/6 + 1/11 ) / ( 1 – 5/66 ) [ putting values ]

= ( 61/66 ) / ( 61/66)

= 1

= tan π/4

Therefore (a+b) = π/4

Answer 2

Step-by-step explanation:

Given :-

$\bf \tan A=\dfrac{5}{6}$

$\bf\tan B =\dfrac{1}{11}$

To Prove :-

$\bf A+B=\dfrac{\pi}{4}$

Solution :-

We know that

$\bf \tan(A+B)=\dfrac{\tan A+\tan B}{1-\tan A.\tan B}$

$\sf \implies \tan(A+B)=\dfrac{\dfrac{5}{6}+\dfrac{1}{11}}{1-\dfrac{5}{6}×\dfrac{1}{11}}$

$\sf\implies \tan(A+B)= \dfrac{\dfrac{55+6}{66}}{1-\dfrac{5}{66}}$

$\sf\implies \tan(A+B)=\dfrac{\dfrac{61}{66}}{\dfrac{66-5}{66}}$

$\sf\implies \tan(A+B)=\dfrac{\dfrac{61}{66}}{\dfrac{61}{66}}$

$\sf\implies \tan(A+B)=\dfrac{61}{66}×\dfrac{66}{61}$

$\sf\implies \tan(A+B)=1$

$\sf\implies (A+B)=\dfrac{\pi}{4}$

Hence

Proved