Please solve this question.

 see proof below

Step-by-step explanation:

Use the Cofunction Identity: sin (90 - A) = cos (A)

Use the Double Angle Identity: sin(2A) = 2 sinA cosA

Use the Triple Angle Identity: cos (3A) = 4cos³A - 3cosA

Use the Zero Product Property: If a · b = 0, then a = 0 or b = 0

Use Pythagorean Identity: cos²A + sin²A = 1  → cos²A = 1 - sin²A

Use Quadratic Formula:  

Proof LHS → RHS:

Assumption:                 Let A = 18°

Multiplication:               then 5A = 5(18°)

                                         →   5A = 90°

Expand:                         2A + 3A = 90°

                                  →  2A = 90° - 3A

Apply sin:                  sin (2A) = sin (90° - 3A)

Cofunction:               sin (2A) = cos (3A)

Double Angle:          2 sinA cos A = cos (3A)

Triple Angle:             2 sin A cos A = 4cos³A - 3cos A

                             → -4cos³A + 3cos A + 2sinA cos A = 0

Factor:                      cos A(-4cos² A + 3 + 2sin A) = 0

Zero Product Property: cos A = 0    or   -4cos² A + 3 + 2sin A = 0

                                             ↓

                                     Disregard (since cos A ≠ 0)

Pythagorean:                                           -4cos² A + 3 + 2sin A = 0

                                                            →  -4(1 - sin² A) + 3 + 2sin A = 0

                                                           →   -4 + 4sin² A + 3 + 2sin A = 0

Simplify:             4sin² A + 2sin A - 1 = 0

                      a=4         b=2      c= -1

none of the above.

for one of the equations to be used in the process, there has to be a term in the equation since squared is .

since there is only a term in the first equation, we cannot derive a from completing the square.

solving with completing the square