What is the general solution for 2sin(a)+csc(a)=3 ?

The general solution for 2sin(a)+csc(a)=3 is a= pi/6+2pin,a=(5pi)/6+2pin,a= pi/2+2pin

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2sin(a)+csc(a)=3

2 sin (a) + csc (a) = 3

a = \frac{π}{6} + 2 πn, a = \frac{5 π}{6} + 2 πn, a = \frac{π}{2} + 2 πn

Solution steps

2 sin (a) + csc (a) = 3

Subtract

3

from both sides

2 sin (a) + csc (a) - 3 = 0

Rewrite using trig identities

- 3 + csc (a) + \frac{2}{csc ( a )} = 0

Solve by substitution

csc (a) = 2, csc (a) = 1

csc (a) = 2 : a = \frac{π}{6} + 2 πn, a = \frac{5 π}{6} + 2 πn

csc (a) = 1 : a = \frac{π}{2} + 2 πn

Combine all the solutions

a = \frac{π}{6} + 2 πn, a = \frac{5 π}{6} + 2 πn, a = \frac{π}{2} + 2 πn

cos (x) = \frac{- 2}{7}

csc (x) = \frac{9}{17}

tan (Θ) = 1.4

sin (x) = 0.51303

t, y = - y + sin (t) + cos (t)

What is the general solution for 2sin(a)+csc(a)=3 ?
The general solution for 2sin(a)+csc(a)=3 is a= pi/6+2pin,a=(5pi)/6+2pin,a= pi/2+2pin