Question

if tan theta = 5/6 and tan theta = 1/11 then theta + theta =

please help me my friends​

Answer 1

Step-by-step explanation:

Proved as described below.

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Explanation:

tan

θ

=

5

6

tan

ϕ

=

1

11

tan

(

θ

+

ϕ

)

=

tan

θ

+

tan

ϕ

1

−

tan

θ

tan

ϕ

=

5

6

+

1

11

1

−

5

6

×

1

11

=

5

×

11

+

1

×

6

6

×

11

6

×

11

−

5

×

1

1

×

6

×

11

=

55

+

6

66

66

−

5

66

=

61

61

=

1

tan

(

θ

+

ϕ

)

=

1

tan

(

π

4

)

=

1

θ

+

ϕ

=

π

4

Answer 2

SOLUTION

$= > \tan(a + b) = \frac{tan \: a + tan \: b}{1 - tan \: a \: tan \: b} \\ \\ = > tan(a + b) = \frac{5}{6} + \frac{1}{11} \div 1 - \frac{5}{6} \times \frac{1}{11} \\ \\ = > tan(a + b) = \frac{55 + 6}{66} \div 1 - \frac{5}{66} \\ \\ = > tan(a + b) = \frac{ \frac{ \frac{61}{66} }{66 - 5} }{66} \\ \\ = > tan(a + b) = \frac{61}{61} \\ \\ = > tan(a + b) = 1 \\ \\ = > a + b = 45 \degree \: \: or \: \: \frac{\pi}{4}$

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