Exponential trigonometrical equation Find x from [-(pi)/(2),(pi)/(2)] in: 2^(sin 3x)-8^(sin x)=sin^3(x) I know that x=0 verifies the equation, but is it the only solution?

Amina Richards

Amina Richards

Answered question

2022-10-30

Exponential trigonometrical equation
Find x from [ π 2 , π 2 ] in:
2 sin 3 x 8 sin x = sin 3 x
I know that x = 0 verifies the equation, but is it the only solution?

Answer & Explanation

Cagliusov8

Cagliusov8

Beginner2022-10-31Added 15 answers

If 2 sin 3 x > 2 3 sin x 4 sin 3 x < 0 sin 3 x < 0 wich is in contradiction with 2 sin 3 x 2 3 sin x > 0 . It is proved equivalently that for 2 sin 3 x < 2 3 sin x sin x > 0 so the equation doesn't have solutions.Finally,the only solution is sin x = 0 x = 0

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