Question

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

Answer 1

tan(a+d)=tan a+tan b/1-tan a×tan b

=1-tan a×tan b

=5/6+1/11 divide1-5/6×1/11

= 61/66 divide 61/66

= 1

= tan1

= 45°

= π\4

LHS= RHS

Answer 2

Given : tan a=5/6 and tanb=1/11

To find : To show that (a+b) = π/4

Solution :

It is proved that (a+b) = π/4

We can simply solve this mathematical problem by using the following mathematical process. [our goal is to calculate the value of (a+b) and then compare it with the desired value of (a+b)]

Here, we will be using general trigonometric formulas.

Now, we know that :

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

By, putting the given values, we get :

$tan(a + b) = \frac{ \frac{5}{6} + \frac{1}{11} }{1 - ( \frac{5}{6} \times \frac{1}{11} ) }$

or,

$\tan(a + b) = \frac{ \frac{55 + 6}{66} }{1 - \frac{5}{66} }$

or,

$\tan(a + b) = \frac{ \frac{61}{66} }{ \frac{61}{66} }$

or,

$\tan(a + b) = \frac{61}{66} \times \frac{66}{61}$

or,

$\tan(a + b) = 1$

or,

$\tan(a + b) = \tan( \frac{\pi}{4} )$

Which implies,

$(a + b) = \frac{\pi}{4}$

(this will be the final step of the given proof)

Hence, it is proved that (a+b) is equal to π/4