Question

given tan A=5÷6 and tan B=1÷11 show that A+B=11÷4​

Answer 1

Answer:

Correct Question:-

• Given tan A = $\dfrac{5}{6}$and tan B = $\dfrac{1}{11}$ show that A + B = $\dfrac{π}{4}$

To Show:-

• A + B = $\dfrac{π}{4}$

Solution:-

As Given,

• tan A = $\dfrac{5}{6}$

• tan B = $\dfrac{1}{11}$

Therefore,

➤ tan (A + B) = $\dfrac{tan A + tan B}{1-tan\:A\:tan\:B}$

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

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

➤ tan (A + B) = 1

As we know tan 45° = 1 which is equal to ${\bold{\dfrac{π}{4}}}$ in radians.

➤ tan (A + B) = $\dfrac{π}{4}$

Hence Proved.

━━━━━━━━━━━━━━━━━━━━━━━━━