Question

If cot a=2 and cot b=3, then what is the value of a+b

Answer 1

$we \: know \\ \cot(a + b) = \frac{ \cot(a) \cot(b) - 1 }{ \cot(a) + \cot(b) } \\ = \frac{2 \times 3 - 1}{2 + 3} = \frac{5}{5} = 1 \\ thus \: \: a + b = 45 \: degrees$

Answer 2

Answer:

45 is the required value of (a+b)

Step-by-step explanation:

Explanation:

Given , cot a = 2...........(i)

and cot b =3.........(ii)

As we know  that $cot (x+y) = \frac{cotx.coty-1}{coty+cotx}$

Step 1:

Adding equation (i) and (ii) we get

cot a+cot b= 2+3

Take common 'cot'

⇒cot(a+b) = 5    ..........(iii)

Step2:

As we know   $cot (x+y) = \frac{cotx.coty-1}{coty+cotx}$

Therefore , write cot(a+b) in this form

⇒  $cot (a+b) = \frac{cota.cotb-1}{cotb+cota}$    ...........(iv)

Now , put the value of cot a =2 and cot b =3  in  equation (iv)

⇒ cot(a+b) = $\frac{(2).(3)-1}{3+2}$

⇒ cot(a+b ) = $\frac{5}{5} =1$

As we know value of cot (45°) is 1.

Therefore , cot(a+b) = 1

⇒cot(a+b) = cot (45°)

⇒ (a+b) = 45

Final answer :

Hence , the value of (a+b) is 45 .