Question

3sin ^2x=2,5sin 2x-1
помогите пожалуйста решить

Answer 1

Ответ:

$3sin(x)^{2} = 2,5sin(2x)-1 \\3sin(x)^{2} = 2*2,5sin(x)cos(x)-1 \\3sin(x)^{2} = 5sin(x)cos(x)-1 \\3sin(x)^{2} - 5sin(x)cos(x) = - 1 (sin(x)^{2} + cos(x)^{2})\\4sin(x) ^{2} - 5sin(x)cos(x) +cos(x)^{2} = 0\\4tan(x)^{2}-5tan(x)+1=0\\4t^{2} -5t+1=0\\t1= 1 и t2=\frac{1}{4} \\ x=\frac{\pi }{4}+k\pi \\ x=arctan(\frac{1}{4} )+k\pi$

Объяснение: