AP EAMCET20224 Jul 2022Evening ShiftMathematicsComplex NumberActual
Multiplicative inverse of the complex number sin θ , cos θ is
Options
- A+ sin θ , + cos θ
- Bsin θ , - cos θ
- Ccos θ , - sin θ
- D- cos θ , sin θ
Correct answer
B. sin θ , - cos θ
Step-by-step solution
We have, z = sin θ + i cos θ Multiplicative inverse of z is 1 z . Now, 1 z = 1 sin θ + i cos θ ⇒ 1 z = 1 sin θ + i cos θ × sin θ - i cos θ sin θ - i cos θ ⇒ 1 z = sin θ - i cos θ sin 2 θ + cos 2 θ ⇒ 1 z = sin θ - i cos θ ∵ sin 2 θ + cos 2 θ = 1 Hence, multiplicative inverse of sin θ , cos θ is sin θ , - cos θ .