If tanA- 5 6- tanB- 1 11- prove that - A-B- 4

Given tan A=56;tan B=111 Consider tan (A+B)=tan A+tan B1 tan Atan B tan(A+B)=56+1111 56111 tan(A+B)=55+66666 566 tan(A+B)=1 A+B=π4 ...

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Byju's Answer

Standard XII

Mathematics

Sin(A+B)Sin(A-B)

If tanA= 5 ...

Question

If $t a n A = \frac{5}{6}$ , $t a n B = \frac{1}{11}$ , prove that : $A + B = \frac{π}{4}$

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Solution

Given $tan A = \frac{5}{6}; tan B = \frac{1}{11}$

Consider $tan (A + B) = \frac{tan A + tan B}{1 - tan A tan B}$

$tan (A + B) = \frac{\frac{5}{6} + \frac{1}{11}}{1 - \frac{5}{6} \frac{1}{11}}$

$tan (A + B) = \frac{\frac{55 + 6}{66}}{\frac{66 - 5}{66}}$

$tan (A + B) = 1$

$A + B = \frac{π}{4}$

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Similar questions

(i) If $t a n A = \frac{5}{6}$ and $t a n B = \frac{1}{11},$ prove that A+B= $\frac{π}{4}$
(ii) If $t a n A = \frac{m}{m - 1}$ and $t a n B = \frac{m}{2 m - 1}$
then prove that $A - B = \frac{π}{4}$

Q. If tan

A = \frac{5}{6},

tan

B = \frac{1}{11},

prove that :

A + B = \frac{π}{4}

Q. If

A + B + C = π

, prove that

tan \frac{A}{2} tan \frac{B}{2} + tan \frac{B}{2} tan \frac{C}{2} + tan \frac{C}{2} tan \frac{A}{2} = 1

Q. If

A = 60^{o}

and

B = 30^{o}

, then prove that

tan (A - B) = \frac{tan A - tan B}{1 + tan A tan B}

Q. If A + B = 225 , prove that tan A + tan B = 1 tanA tanB

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If tanA=56, tanB=111, prove that : A+B=π4

Given tanA=56;tanB=111Consider tan(A+B)=tanA+tanB1−tanAtanBtan(A+B)=56+1111−56111tan(A+B)=55+66666−566tan(A+B)=1A+B=π4

If $t a n A = \frac{5}{6}$ , $t a n B = \frac{1}{11}$ , prove that : $A + B = \frac{π}{4}$

Given $tan A = \frac{5}{6}; tan B = \frac{1}{11}$

Consider $tan (A + B) = \frac{tan A + tan B}{1 - tan A tan B}$

$tan (A + B) = \frac{\frac{5}{6} + \frac{1}{11}}{1 - \frac{5}{6} \frac{1}{11}}$

$tan (A + B) = \frac{\frac{55 + 6}{66}}{\frac{66 - 5}{66}}$

$tan (A + B) = 1$

$A + B = \frac{π}{4}$