What is the general solution for 5-7sin(A)-2cos^2(A)=0 ?

The general solution for 5-7sin(A)-2cos^2(A)=0 is A= pi/6+2pin,A=(5pi)/6+2pin

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5-7sin(A)-2cos^2(A)=0

5 - 7 sin (A) - 2 cos^{2} (A) = 0

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

Solution steps

5 - 7 sin (A) - 2 cos^{2} (A) = 0

Rewrite using trig identities

3 + 2 sin^{2} (A) - 7 sin (A) = 0

Solve by substitution

sin (A) = 3, sin (A) = \frac{1}{2}

sin (A) = 3 :

No Solution

sin (A) = \frac{1}{2} : A = \frac{π}{6} + 2 πn, A = \frac{5 π}{6} + 2 πn

Combine all the solutions

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

x, ln (y) + y^{2} = sin (x) + c

\frac{5}{2} = 2 + cos (x + \frac{2 π}{3})

sin (x) + cos (x) = \frac{2 + 3}{2}

2 sec (x) = 0

sin^{2} (θ) cos^{2} (θ) = 0, 0 \leq θ < 2 π

What is the general solution for 5-7sin(A)-2cos^2(A)=0 ?
The general solution for 5-7sin(A)-2cos^2(A)=0 is A= pi/6+2pin,A=(5pi)/6+2pin