Find all solutions of the question.

Question

8 sin x - 9sqrt(2) = 6 sin x - 8sqrt(2)

Answer 1

This is not Calculus question.

8 sin x - 9 √2 = 6 sin x - 8 √2

Subtract 6 sin x to both sides

2 sin x - 9 √2 = - 8 √2

Add 9 √2 to both sides

2 sin x = √2

sin x = √2 / 2

On interval 0 to 2 π sin x = √2 / 2 for x = 45° = π / 4 rad

and

x = 135° = 3 / 4 π rad

Period of sin x is 2 π rad so the solutions are:

x = π / 4 + 2 π n

and

x = 3 / 4 π + 2 π n

where

n = ± 1 , ± 2 , ± 3...

By the way √2 / 2 is the same as 1 / √2 becouse:

√2 / 2 = √2 / √2 ∙ √2 = 1 / √2

Answer 2

My typo.

n = 0 , ± 1 , ± 2 , ± 3...