solvefor α,cos^2(α)+cos^2(β)=1

Solution

solve for

α, cos^{2} (α) + cos^{2} (β) = 1

α = arccos (- sin (β)) + 2 πn, α = - arccos (- sin (β)) + 2 πn, α = arccos (sin (β)) + 2 πn, α = - arccos (sin (β)) + 2 πn

Solution steps

cos^{2} (α) + cos^{2} (β) = 1

Subtract

1

from both sides

cos^{2} (α) + cos^{2} (β) - 1 = 0

Rewrite using trig identities

cos^{2} (α) - sin^{2} (β) = 0

Factor

cos^{2} (α) - sin^{2} (β) : (cos (α) + sin (β)) (cos (α) - sin (β))

(cos (α) + sin (β)) (cos (α) - sin (β)) = 0

Solving each part separately

cos (α) + sin (β) = 0 or cos (α) - sin (β) = 0

cos (α) + sin (β) = 0 : α = arccos (- sin (β)) + 2 πn, α = - arccos (- sin (β)) + 2 πn

cos (α) - sin (β) = 0 : α = arccos (sin (β)) + 2 πn, α = - arccos (sin (β)) + 2 πn

Combine all the solutions

α = arccos (- sin (β)) + 2 πn, α = - arccos (- sin (β)) + 2 πn, α = arccos (sin (β)) + 2 πn, α = - arccos (sin (β)) + 2 πn

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

sin (x + 3 0^{\circ}) = \frac{1}{2}

sin (θ) = 21

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

y, arcsin (y) = arcsin (x)