2(1-2sin^2x)+7sinx-5=0
sinx=t
-4t^2+7t-3=0
D=49-48=1
t1=(-7+1)/-8=3/4 sinx=3/5; x1= arcsin(3/4)+2pi; x2=pi-arcsin(3/4)+2pil
t2=(-7-1)/-8=1 sinx=1; x3=pi/2+2pik
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Answers & Comments
2cos²x-2sin²x-7sinx-5=0
2-2sin²x-2sin²x+7sinx-5=0
-4sin²x+7sinx-3=0
sinx=t€[-1;1]
4t²-7t+3=0
D=49-48=1
t=(7±1)/8
t1=1;t2=3/4
sinx=1;x=π/2+2πk:k€Z
sinx=3/4;x=(-1)ⁿarcsin3/4+πn;n€Z
Verified answer
2(1-2sin^2x)+7sinx-5=0
sinx=t
-4t^2+7t-3=0
D=49-48=1
t1=(-7+1)/-8=3/4 sinx=3/5; x1= arcsin(3/4)+2pi; x2=pi-arcsin(3/4)+2pil
t2=(-7-1)/-8=1 sinx=1; x3=pi/2+2pik