Csc^2x+cot^2x=3; 0 less than equal to x less than equal to 2pi

csc2xcot2x3

#1

csc^2x+cot^2x=3; 0 less than equal to x less than equal to 2pi

Answer:

Use the trigonometric identity csc^2x-cot^2x=1 ;

csc^2x+cot^2x=3
=>(1+cot^2x)+cot^2x=3
=>1+2cot^2x = 3
=>2cot^2x = 2
=>cot^2x=1
=>cot^2x-1=0
=>(cotx+1)(cotx-1)=0 (By factorisation or roots can be written by solving the quadratic)
=> cotx = 1 or cotx = -1
=> x= pi/4 , 5pi/4 or x = 3pi/4,7pi/4