Question

If sin A = 4/5 find the value of cot A + tan A.​

Answer 1

The answer is 2

Explanation:

`Cot(x)=(1)/(tan(x)) =(Cos(x))/(Sin(x))`

`Tan(x) = (Sin(x))/(Cos(x))`

`Cos((\pi )/(2) -x)=sin(x)`

This means that

`(\cos \left((\pi )/(2)-(4)/(5)\right))/(\sin \left((4)/(5)\right))+(\sin \left((4)/(5)\right))/(\cos \left((\pi )/(2)-(4)/(5)\right))`

This will be a long one to solve
-> apply cos identity to right side

`(\cos \left((\pi )/(2)-(4)/(5)\right))/(\sin \left((4)/(5)\right))+(\sin \left((4)/(5)\right))/(\cos \left((\pi )/(2)\right)\cos \left((4)/(5)\right)+\sin \left((\pi )/(2)\right)\sin \left((4)/(5)\right))`

-> simplify according to unit circle

`(\cos \left((\pi )/(2)-(4)/(5)\right))/(\sin \left((4)/(5)\right))+1`

->apply cos identity again

`(\cos \left((\pi )/(2)\right)\cos \left((4)/(5)\right)+\sin \left((\pi )/(2)\right)\sin \left((4)/(5)\right))/(\sin \left((4)/(5)\right))+1`

If you apply for unit circle numbers,

you will get 2

I do not recommend using a calculator for these questions, but instead, turn the form into
`sin(\pi )/(2)` other base unit circle locations, and most likely this is the method that your teacher counts as "right."
when using a calculator, it tends to "round" the number, which result in a inaccurate answer

Answer 2

2.08

Explanation:

`sin^(-1) 4/5 = 53.13\\tan 53.13 = 1.33\\cot 53.13 = 0.75\\1.33 + 0.775 = 2.08`