What is the general solution for cos^2(a)+2sin(a)+1=0 ?

The general solution for cos^2(a)+2sin(a)+1=0 is a=-0.82132…+2pin,a=pi+0.82132…+2pin

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cos^2(a)+2sin(a)+1=0

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

a = - 0.82132 \dots + 2 πn, a = π + 0.82132 \dots + 2 πn

Solution steps

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

Rewrite using trig identities

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

Solve by substitution

sin (a) = 1 - 3, sin (a) = 1 + 3

sin (a) = 1 - 3 : a = arcsin (1 - 3) + 2 πn, a = π + arcsin (- 1 + 3) + 2 πn

sin (a) = 1 + 3 :

No Solution

Combine all the solutions

a = arcsin (1 - 3) + 2 πn, a = π + arcsin (- 1 + 3) + 2 πn

Show solutions in decimal form

a = - 0.82132 \dots + 2 πn, a = π + 0.82132 \dots + 2 πn

tan (x) = \frac{5}{15}

2 sin (x + \frac{π}{9}) = - 1

1 + cos (a) = \frac{3 + 4 cos ( a )}{2}

3 cos (x) - 2 cos^{2} (x) = 0, 0^{\circ} < x < 36 0^{\circ}

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

What is the general solution for cos^2(a)+2sin(a)+1=0 ?
The general solution for cos^2(a)+2sin(a)+1=0 is a=-0.82132…+2pin,a=pi+0.82132…+2pin