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

The general solution for tan^2(γ)+1=cos^2(γ) is γ=2pin,γ=pi+2pin

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tan^2(γ)+1=cos^2(γ)

tan^{2} (γ) + 1 = cos^{2} (γ)

γ = 2 πn, γ = π + 2 πn

Solution steps

tan^{2} (γ) + 1 = cos^{2} (γ)

Subtract

cos^{2} (γ)

from both sides

tan^{2} (γ) + 1 - cos^{2} (γ) = 0

Rewrite using trig identities

- \frac{1}{sec ^{2} ( γ )} + sec^{2} (γ) = 0

Solve by substitution

sec (γ) = 1, sec (γ) = - 1, sec (γ) = i, sec (γ) = - i

sec (γ) = 1 : γ = 2 πn

sec (γ) = - 1 : γ = π + 2 πn

sec (γ) = i :

No Solution

sec (γ) = - i :

No Solution

Combine all the solutions

γ = 2 πn, γ = π + 2 πn

sin^{2} (x) + 8 sin (x) - 9 = 0

- 2 sin^{2} (θ) + 10 sin (θ) - 3 = 3 sin (θ), 0^{\circ} \leq θ < 36 0^{\circ}

cot^{2} (θ) + 4 csc (θ) = - 5

10 sin (a) + 7 sin (a) + 1 sin (a) + 8 sin (a) = 48

2 cos^{2} (θ) + 7 sin (θ) = 5

What is the general solution for tan^2(γ)+1=cos^2(γ) ?
The general solution for tan^2(γ)+1=cos^2(γ) is γ=2pin,γ=pi+2pin