Question

How do you solve `secxcscx=2cscx` and find all solutions in the interval `[0,2pi)`?

Answer 1

`cos x = pi/3 and cos x = (5pi)/3`

Explanation:

=>`1/cos x * 1/ sin x = 2 1/sin x`
=>`1/cos x * cancel(1/ sin x) = 2 cancel(1/sin x )`
=>`cos x = 1/2`
=>`cos x = cos (pi/3)`...[Ans]

cos is positive at `I` quadrant and `IV` quadrant
so for `IV` quadrant, angle will be `(2pi - theta)`

`cos x = cos (2pi-theta)`

`cos x = cos (2pi-(pi/3))`

`cos x = cos ((5pi)/3)`... [Ans]