What is the general solution for (1+tan^2(x))cos^2(x)=sec(x) ?

The general solution for (1+tan^2(x))cos^2(x)=sec(x) is x=2pin

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(1+tan^2(x))cos^2(x)=sec(x)

(1 + tan^{2} (x)) cos^{2} (x) = sec (x)

x = 2 πn

Solution steps

(1 + tan^{2} (x)) cos^{2} (x) = sec (x)

Subtract

sec (x)

from both sides

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

Rewrite using trig identities

- sec (x) + 1 = 0

Move

1

to the right side

- sec (x) = - 1

Divide both sides by

- 1

sec (x) = 1

General solutions for

sec (x) = 1

x = 0 + 2 πn

Solve

x = 0 + 2 πn : x = 2 πn

x = 2 πn

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

cos^{6} (x) = - cos^{2} (x)

2 sin^{3} (x) - 5 sin^{2} (x) + 2 sin (x) = 0

\frac{cos ^{2} ( a ) - 3 cos ( a ) + 2}{sin ^{2} ( a )} = 1

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

What is the general solution for (1+tan^2(x))cos^2(x)=sec(x) ?
The general solution for (1+tan^2(x))cos^2(x)=sec(x) is x=2pin