Solve the equation secx cscx = 2secx

Question

Answer 1

secx(cscx) = 2secx

secx(cscx) - 2secx = 0

factor

secx(cscx -2) =0

set each factor = 0

secx = 0 has no solution, since secant of any angle can never be between -1 and +1

cscx =2

1/sinx = 2

sinx = 1/2

x = sin^-1(1/2)

= 30 +360n degrees where n= any integer

or x= pi/6 +2npi where n = any integer

check the answer

secx(cscx) = 2secx

sec30(csc30) = 2sec30

csc30 = 2sec30/sec30 = 2

csc30 = 2

1/sin30 =2

sin30 = 1/2

a 30-60-90 degree right triangle has 3 sides 1-sqr3 - 2

sin30 = opposite side/hypotenuse = 1/2