What is the general solution for sin^2(a)sec(a)=tan^2(a) ?

The general solution for sin^2(a)sec(a)=tan^2(a) is a=2pin,a=pi+2pin

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sin^2(a)sec(a)=tan^2(a)

sin^{2} (a) sec (a) = tan^{2} (a)

a = 2 πn, a = π + 2 πn

Solution steps

sin^{2} (a) sec (a) = tan^{2} (a)

Subtract

tan^{2} (a)

from both sides

sin^{2} (a) sec (a) - tan^{2} (a) = 0

Express with sin, cos

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

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

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

Factor

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

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

Solving each part separately

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

sin^{2} (a) = 0 : a = 2 πn, a = π + 2 πn

cos (a) - 1 = 0 : a = 2 πn

Combine all the solutions

a = 2 πn, a = π + 2 πn

tan^{2} (θ) - sec (θ) = 1

sin (x) = \frac{8}{10}

sin (x) cos (2 x) + cos (x) sin (2 x) = 0

7 cos (5 x) + 9 = 12

cos (2 x) + 1 = sin (2 x)

What is the general solution for sin^2(a)sec(a)=tan^2(a) ?
The general solution for sin^2(a)sec(a)=tan^2(a) is a=2pin,a=pi+2pin