Question

Question #a18e0

Answer 1

`{pi/6,pi/3,(7pi)/6,(4pi)/3}`

Explanation:

we want the solution set for

`2sin2theta=sqrt3," "0<=theta<2pi`

`2sin2theta=sqrt3=>sin2theta=sqrt3/2`

`2theta=sin^(-1)(sqrt3/2)`

the principal value is `2theta=pi/3`

the complementary value is `pi-pi/3=(2pi)/3`

we want the values for theta in the given range

consider the principal value , and add `2pis` since sine is periodic with period `2pi`

`2theta= pi/3, (7pi)/3,(13pi)/3,...`

`theta=pi/6, (7pi)/6,color(red)((13pi)/6,...)`

values in right and onwards are outside the required range

likewise consider the complementary value

`2theta=(2pi)/3, (8pi)/3,(14pi)/3....`

`:.theta=pi/3,(4pi)/3,color(red)((7pi)/3,..`

so the solution set

`{pi/6,pi/3,(7pi)/6,(4pi)/3}`