1.

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

Answer»

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.

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