Answer:
Step-by-step explanation:
A trigonometric equation is given to us , and we need to find the solutions of the equation within the interval [ 0,2π ]
The given equation is ,
Add -7 to both sides ,
Divide both sides by 5 ,
Simplify ,
Now solve for x ,
Simplify ,
The secant function is <u>negative in the second and third quadrants. </u> Subtracting the reference angle from <u>2</u><u>π</u><u> </u> to find the solution in the third quadrant to find the solution second solution.
Simplify ,
Now here the period of sec x is <u>2</u><u>π</u> . Therefore ,
Therefore all the possible solutions are ,
<u>Hence</u><u> the</u><u> </u><u>required</u><u> </u><u>answer</u><u> </u><u>is </u><u>2</u><u>π</u><u>/</u><u>3 </u><u>and </u><u>4</u><u>π</u><u>/</u><u>3.</u>