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

The general solution for 1+cos^2(x^2+1)=sin^2(x^2+1) is x=sqrt((pi+2pin-2)/2),x=-sqrt((pi+2pin-2)/2)

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

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

x = \frac{π + 2 πn - 2}{2}, x = - \frac{π + 2 πn - 2}{2}

Solution steps

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

Subtract

sin^{2} (x^{2} + 1)

from both sides

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

Rewrite using trig identities

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

Move

1

to the right side

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

General solutions for

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

2 (1 + x^{2}) = π + 2 πn

Solve

2 (1 + x^{2}) = π + 2 πn : x = \frac{π + 2 πn - 2}{2}, x = - \frac{π + 2 πn - 2}{2}

x = \frac{π + 2 πn - 2}{2}, x = - \frac{π + 2 πn - 2}{2}

2 sin^{2} (x) + sin (x) - 6 = 0

tan (θ) = \frac{8}{15}, sin (θ) > 0

cos (x) = \frac{86.6}{100}

- 2 cos^{2} (θ) - 8 cos (θ) - 1 = - 5 cos (θ)

- 6 sin (θ) = - 33

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