2015 · Q62
If cos A = tan B, cos B = tan C and cos C = tan A, then sin A is equal to
Elementary MathematicsTrigonometry
- A(√5 − 1)/4
- B(√5 − 1)/2
- C(√3 − 1)/4
- D(√3 − 1)/2
Explanation
cosA = tanB gives cosA·cosB = sinB, and cyclically; the symmetric system forces A = B = C (each step is a contraction), so cos²A = sinA, i.e. sin²A + sinA − 1 = 0, giving sinA = (√5−1)/2 (option B).