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

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

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cos^2(x)=(1-tan^2(x))/(sec^2(x))

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

x = πn

Solution steps

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

Subtract

\frac{1 - tan ^{2} ( x )}{sec ^{2} ( x )}

from both sides

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

Simplify

cos^{2} (x) - \frac{1 - tan ^{2} ( x )}{sec ^{2} ( x )} : \frac{cos ^{2} ( x ) sec ^{2} ( x ) - 1 + tan ^{2} ( x )}{sec ^{2} ( x )}

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

\frac{f ( x )}{g ( x )} = 0 \Rightarrow f (x) = 0

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

Rewrite using trig identities

tan^{2} (x) = 0

Apply rule

x^{n} = 0 \Rightarrow x = 0

tan (x) = 0

General solutions for

tan (x) = 0

x = 0 + πn

Solve

x = 0 + πn : x = πn

x = πn

sin^{2} (x) - 3 cos (x) - 4 = 0

tan^{2} (x) + sec (x) = 5

4 sin^{5} (x) = 3

cos (\frac{x}{2}) = 0.5

sin (x + 6 0^{\circ}) = 2 cos (x)

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