What is the general solution for 2sec(x)cos^2(x)=csc^2(x)-cot^2(x) ?

The general solution for 2sec(x)cos^2(x)=csc^2(x)-cot^2(x) is x= pi/3+2pin,x=(5pi)/3+2pin

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2sec(x)cos^2(x)=csc^2(x)-cot^2(x)

2 sec (x) cos^{2} (x) = csc^{2} (x) - cot^{2} (x)

x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

Solution steps

2 sec (x) cos^{2} (x) = csc^{2} (x) - cot^{2} (x)

Subtract

csc^{2} (x) - cot^{2} (x)

from both sides

2 cos^{2} (x) sec (x) - csc^{2} (x) + cot^{2} (x) = 0

Rewrite using trig identities

\frac{2}{sec ( x )} - 1 = 0

Multiply both sides by

sec (x)

2 - sec (x) = 0

Move

2

to the right side

- sec (x) = - 2

Divide both sides by

- 1

sec (x) = 2

Verify Solutions

Find undefined (singularity) points:

sec (x) = 0

Combine undefined points with solutions:

sec (x) = 2

General solutions for

sec (x) = 2

x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

1 = 7 cos (\frac{π}{3} t)

12 cos^{2} (x) + 2 cos (x) - 2 = 0

sin (θ) = - 0.94

sin (θ) = 0, 0 \leq θ \leq 2 π

sin (θ) = - 0.71

What is the general solution for 2sec(x)cos^2(x)=csc^2(x)-cot^2(x) ?
The general solution for 2sec(x)cos^2(x)=csc^2(x)-cot^2(x) is x= pi/3+2pin,x=(5pi)/3+2pin