RRB Junior Engineer / DMS / CMA 2019 · Question 23 of 3719

If x = r sin A cos B, y = r sin A sin B and z = r cos A, then find x² + y² + z².

Mathematics - Trigonometry

Aa. 2r²
Bb. 3/2 r²
Cc. r²Correct
Dd. r²(cos² B + cos² A)

Answer: C. c. r²

Explanation

x = r sin A cos B, y = r sin A sin B z = r cos A Now, x² + y² + z² = (r sin A cos B) ² + (r sin A sin B) ² + (r cos 2A) = r2 sin2 A (cos² B + sin² B) +2 rcos² A = r² sin² A +2 rcos² A = r² (sin² A + cos² A) = r2

Source: RRB JE 2019 CBT-1 (24-May-2019 Shift-2) — ixambee compilation with answer key and solutions · reliable-secondary

Practice the full RRB Junior Engineer / DMS / CMA 2019 paper

Timed test with all 3719 questions, just like the real exam.

Start test