Find the principal solutions of the following equations : `sinx=(1)/(2)`

Options

A. `pi/6`
B. `pi/6, (5pi)/6`
C. `pi/6, -pi/6`
D. None of these

Answer

B

Explanation

(i) The given equation is sin `x=(1)/(2)`.
We know that `"sin"(pi)/(6)=(1)/(2)andsin(pi-(pi)/(6))=(1)/(2)`.
`therefore "sin"(pi)/(6)=(1)/(2)and"sin"(5pi)/(6)=(1)/(2)`.
Hence , the principal solutions are `x=(pi)/(6)andx=(5pi)/(6)`.
(ii) The given equation is cos x `=(1)/(sqrt(2))`.
We know that `"cos"(pi)/(4)=(1)/(sqrt(2))andcos(2pi-(pi)/(4))=(1)/(sqrt(2))`.
`therefore"cos"(pi)/(4)=(1)/(sqrt(2))and "cos"(7pi)/(4)=(1)/(sqrt(2))`.
Hence , the principal solutions are `x=(pi)/(4)and x = (7pi)/(4)`.
(iii) The given equation is tan `x=(1)/(sqrt(3))`.
We know that tan `(pi)/(6)=(1)/(sqrt(3))and tan (pi+(pi)/(6))=(1)/(sqrt(3))`.
`therefore "tan"(pi)/(6)=(1)/(sqrt(3))and" tan"(7pi)/(6)=(1)/(sqrt(3))`.
Hence , the principal solutions are `x=(pi)/(6) andx=(7pi)/(6)`.