What is the general solution for (1+cos^2(a))sin^2(a)=1 ?

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

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(1+cos^2(a))sin^2(a)=1

(1 + cos^{2} (a)) sin^{2} (a) = 1

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

Solution steps

(1 + cos^{2} (a)) sin^{2} (a) = 1

Subtract

1

from both sides

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

Rewrite using trig identities

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

Solve by substitution

sin (a) = 1, sin (a) = - 1

sin (a) = 1 : a = \frac{π}{2} + 2 πn

sin (a) = - 1 : a = \frac{3 π}{2} + 2 πn

Combine all the solutions

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

cos^{4} (x) = cos^{23} (x)

cos^{4} (x) + 2 cos^{2} (x) = 1

cos^{2} (x) + sin^{2} (x) = cos^{5} (x)

sin (x - 4 5^{5}) = \frac{( 2 )}{2}

\frac{sin ( x ) - 3 \cdot cos ( x )}{2} = 0

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