Question

Evaluate? `tan(55^@-A) - cot(35^@ - A)`

`tan(55^@-A) - cot(35^@ - A)`

Answer 1

`(-2tan 2A)/(cos 55)`

Explanation:

f(A) = tan (55 - A) - cot (35 - A)
Note that cot (35 - A) = tan (90 - (35 - A) = tan (55 + a)
f(A ) = tan (55 - A) - tan (55 + A)
Use trig identity:
`tan a - tan b = (sin (a - b))/(cos a.cos b)`
In this case:
`sin (a - b) = sin (55 - A - 55 - A) = sin (-2A) = - sin 2A`
`cos a.cos b = cos (55 - A).cos (55 + A) = (1/2)cos 55.cos 2A`
Finally
`f(A) = - (2tan 2A)/(cos 55)`