Question

5.
If cosec A + cot A =
11
then tan A is equal to-​

Answer 1

Answer:

cosecA +cotA =11/2 

or 1/sinA + cosA/sinA = 11/2 

or 1+ cosA/sinA = 11/2 

2 cos^2A/ 2 / 2sinA/ cosA/2 = 11/2 

cotA/2 =11/2 

so tanA/2 = 2/11 

so tanA = 2 tanA/2/( 1- tan^2A/2 

={ 2* 2/11}/( 1- 4/121) 

= (4/11)/ (117/121) 

=4/11* 121/117 

=44/117

Step-by-step explanation:

Following 3 formulas are useful to solve this:

cos(A) = 2 (cosA/2)^2 - 1

sin(A) = 2 sin(A/2) cos(A/2)

tan(A) = 2tanA/2 / (1 - (tanA/2)^2)

cosecA + cotA = 11/2

=> 1/sin(A) + cos(A)/sin(A) = 11/2

=> 1/sin(A)(1 + cos(A)) = 11/2

=> (1 + cos(A)) / sin(A) = 11/2

=> 2(cosA/2)^2 / sin(A) = 11/2

=> 2(cosA/2)^2 / 2sin(A/2)cos(A/2) = 11/2

=> 1 / tan(A/2) = 11/2

=> tan(A/2) = 2/11

=> tan(A) = (4 / 11) (1 - 4/121)

tan(A) = (4 / 11) (1 - 4/121)= (4 / 11) (117 / 121)

tan(A) = (4 / 11) (1 - 4/121)= (4 / 11) (117 / 121)= 4 * 121 / 11 * 117

tan(A) = (4 / 11) (1 - 4/121)= (4 / 11) (117 / 121)= 4 * 121 / 11 * 117= 44/117

Hope it will help you

Mark the brainliest

Answer 2

Answer:

1/11-cosecA

Step-by-step explanation:

cosecA +cotA=11

therefore,cotA=11-cosec A

As cotA=1/tan A

so 1/cotA=1/11-cosecA

=tan A=1/11-cosecA