SOLUTION: Find all the angles between 0� to 360� inclusive which satisfy the equation i) 2cot^2x + 5 = 7cosecx ii) 2cos^2x + 3sinx = 3

Question 217322: Find all the angles between 0� to 360� inclusive which satisfy the equation
i) 2cot^2x + 5 = 7cosecx ii) 2cos^2x + 3sinx = 3
Answer by chibisan(131) (Show Source): You can put this solution on YOUR website!
i)
cot^2x = cosec^2x -1
2cot^2+5=7cosecx
2(cosec^2x-1)+5 = 7cosecx
2cosec^2x -2 + 5 = 7cosecx
2cosec^2x -7cosecx +3 = 0
(2cosecx-1)(cosecx - 3)= 0
cosecx = 1/2
1/sinx = 1/2
sinx = 2
(no solution)
cosecx=3
1/sinx = 3
sinx =1/3
x = 19.5� , 180 - 19.5�
x = 19.5 , 160.5� (ans)

ii)
2cos^2x + 3sinx = 3
2(1-sin^2x) + 3sinx - 3=0
-2sin^2x + 3sinx + 1= 0
0= 2sin^2x - 3sinx + 1
0= (2sinx- 1)(sinx - 1)
sinx = 1/2
x = 30� , 180 - 30�
x = 30� , 150�
sinx =1
x= 90�, 180�-90�
x = 90�
x= 30� , 90� , 150� (ans)
RELATED QUESTIONS
Find all the angles between 0 degrees and 360 inclusive which satisfy the equation... (answered by stanbon)

how to find all the angles between 0 and 360 which satisfy the equation sin(2x+10)=0.5 (answered by Alan3354)

Find all the angles between 0� and 360� inclusive which satisfy the equation 4sin2x -... (answered by ikleyn)

Find all the angles between 0� and 360� inclusive which satisfy the equation... (answered by Edwin McCravy)

Find all real numbers in the interval [0, 2pi) that satisfy each equation. 1.... (answered by lwsshak3)

Find all the angles between 0� and 360� inclusive which satisfy the equation 4sin^2(x) -... (answered by htmentor)

Find all solutions in the interval [0,2pi)... (answered by MathLover1)

8 sin^2 x + 3 sin 2x = 4 Solve for all angles btw 0 and 360 which satisfy the equation. (answered by ikleyn)

2cos^2x-3sinx-3=0 (answered by ikleyn)