Question

Find the value of 11cosecA- 11cotA ?​

Answer 1

1) Find the value of 11cosecA- 11cotA ?

Step-by-step explanation:

Following 3 formulas will be handy 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

Using eqn 1 above

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

Using eqn 2

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

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

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

Using eqn 3

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

= (4 / 11) (117 / 121)

= 4 * 121 / 11 * 117

= 44/117