2sin([tex] \frac{7 \pi }{2} [/tex]-x)*sinx=cosx на [[tex] \frac{7 \pi }{2} [/tex];5[tex] \pi [/tex]]. Created by reygenn. algebra-ru

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reygenn @reygenn

July 2022 1 8 Report

2sin([tex] \frac{7 \pi }{2} [/tex]-x)*sinx=cosx на [[tex] \frac{7 \pi }{2} [/tex];5[tex] \pi [/tex]]

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sedinalana

Verified answer

2sin(7π/2-x)*sinx=cosx
-2cosx*sinx-cosx=0
-cosx(2sinx+1)=0
cosx=0⇒x=π/2+πn,n∈z
7π/2≤π/2+πn≤5π
7≤1+2n≤10
6≤2n≤9
3≤n≤4,5
n=3⇒x=π/2+3π=7π/2
n=4πx=π/2+4π=9π/2
sinx=-1/2⇒x=-π/6+2πn U x=-5π/6+2πn
7π/2≤-π/6+2πn≤5π
21≤-1+12n≤30
22≤12n≤31
11/6≤n≤31/12
n=2⇒x=-π/6+4π=23π/24
7π/2≤-5π/6+2πn≤5π
21≤-5+12n≤30
26≤12n≤35
13/6≤n≤35/12
нет решения

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