Answer:
1/2
Explanation:
Given right triangle ABC with right angle A and tan(B) = 1, you want the value of the expression tan(C) -sin(B)cos(C).
Angles
Angle A is given as 90°.
Angle B is found from ...
tan(B) = 1 ⇒ B = arctan(1) = 45°
Angle C is its complement:
C = 90° -B = 45°
Trig functions
The relevant trig functions are ...
tan(C) = tan(45°) = 1
sin(B) = sin(45°) = 1/√2
cos(C) = cos(45°) = 1/√2
Expression
Then the value of the expression is ...
tan(C) -sin(B)cos(C)
= 1 -(1/√2)(1/√2) = 1 -1/2
= 1/2