tan200(cot10-tan10)
sorry about the double-post
proof of above:
tan200(cot10-tan10)
= tan20(1/tan10 - tan10) , 9since by CAST tan200 = tan200)
= tan20( 1 - tan^2 10)/tan10
= 2tan10/(1 - tan^2 10) * ( 1 - tan^2 10)/tan10
= 2
Khavdaila answer
To simplify the expression tan(200°) * (cot(10°) - tan(10°), we can first evaluate the trigonometric functions.
tan(200°):
We can use the periodicity of the tangent function to find an equivalent angle within the range of [-90°, 90°].
200° is greater than 90°, so we can subtract 180° to get an equivalent angle in the range:
200° - 180° = 20°
Now we can evaluate tan(20°).
cot(10°):
To simplify cot(10°), we can use the identity cot(x) = 1/tan(x). Therefore, cot(10°) can be simplified to 1/tan(10°).
tan(10°):
Now we can evaluate tan(10°).
Now that we have the values of tan(20°) and tan(10°), we can substitute them back into the expression:
tan(200°) * (cot(10°) - tan(10°)) becomes tan(20°) * (1/tan(10°) - tan(10°)).
Now we can plug in the values we found earlier:
tan(20°) * (1/tan(10°) - tan(10°)) = tan(20°) * (1/(tan(10°)) - tan(10°)).
Alternatively, if you have a calculator or a tool that can directly evaluate trigonometric functions, you can input the original expression and get an approximate numerical value.
Good
keystrokes I used on my SHARP scientific calculator
I assume your units are degrees, so make sure your calc is set to DEG
1÷
tan 10
-
tan 10 =
x
ta200
=
you should get 2