What is the general solution for cos(x)sin(x)cos(x)=1-sin^2(x) ?

The general solution for cos(x)sin(x)cos(x)=1-sin^2(x) is x= pi/2+2pin,x=(3pi)/2+2pin

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cos(x)sin(x)cos(x)=1-sin^2(x)

cos (x) sin (x) cos (x) = 1 - sin^{2} (x)

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

Solution steps

cos (x) sin (x) cos (x) = 1 - sin^{2} (x)

Subtract

1 - sin^{2} (x)

from both sides

cos^{2} (x) sin (x) - 1 + sin^{2} (x) = 0

Rewrite using trig identities

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

Factor

- cos^{2} (x) + cos^{2} (x) sin (x) : cos^{2} (x) (sin (x) - 1)

cos^{2} (x) (sin (x) - 1) = 0

Solving each part separately

cos^{2} (x) = 0 or sin (x) - 1 = 0

cos^{2} (x) = 0 : x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn

sin (x) - 1 = 0 : x = \frac{π}{2} + 2 πn

Combine all the solutions

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

sin (θ) = 1 - (1 - (cos (θ) - 1)^{2})

5 cos (x) - 3 sin (x) = 4

14.79 m = (\frac{7.6 1 _{0}^{2} sin ( 2 θ _{0} )}{g})

2 cos (x) + 3 cos (x) - 2 = 0

sec (\frac{5 θ}{4}) = 2, [0.2 π]

What is the general solution for cos(x)sin(x)cos(x)=1-sin^2(x) ?
The general solution for cos(x)sin(x)cos(x)=1-sin^2(x) is x= pi/2+2pin,x=(3pi)/2+2pin