Question

What does `4sin(arc tan(-7))-2cot(arccot(4))` equal?

Answer 1

`=-113/(17 sqrt 50)`

Explanation:

Let `a = arc tan (-7) in (-pi/2, 0)`.

Then, `sin a =-7/sqrt 50 and cos a=1/sqrt 50`.

Let `b = arc cot(4) in (0, pi/2)`.

Also, `2b in (0, pi/2)`

Then, `sin b= 1/sqrt 17, cos b = 4/sqrt 17`,

`sin 2b = 2 sin b cos b = 8/17` and

`cos 2b =2 cos^2 b - 1 = 15/17`.

Now, the given expression is

`4 sin (a - 2b)`

`=4(sina cos 2b- cos a sin 2b)`

`=4((-7/sqrt 50)(15/17)-(1/sqrt 50)(8/17)`

`=-113/(17 sqrt 50)`.