Question

In right triangle ABC, m∠B is not equal to m∠C. Let sin(B) = r and cos(B) = s. What is sin(C) - cos(C)?

a) r + s
b) s - r
c) r - s
d) s + r

Answer 1

To find sin(C) - cos(C) in a right triangle ABC where m∠B is not equal to m∠C and sin(B) = r and cos(B) = s, we can use the trigonometric identity sin²(B) + cos²(B) = 1 to find sin(C) and cos(C). Substituting sin(B) and cos(B), we can simplify the expression to √(1 - s²) - s.

Step-by-step explanation:

To find sin(C) - cos(C), we can use the fact that the sum of the angles in a triangle is always 180 degrees. Since m∠B is not equal to m∠C, we know that the angles in triangle ABC are A, B, and C.

Since sin(B) = r and cos(B) = s, we can use the trigonometric identity sin²(B) + cos²(B) = 1 to find sin(C) and cos(C). Subtracting cos²(B) from both sides gives:

sin²(B) = 1 - cos²(B)

Rewriting sin(C) and cos(C) using sin(B) and cos(B) gives:

sin(C) = sin(A) = √(1 - cos²(B)) = √(1 - s²)

cos(C) = cos(A) = s

Therefore, sin(C) - cos(C) = √(1 - s²) - s