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Стрілець140
@Стрілець140
August 2022
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Обчислити sinx(3-4sin^2x)/cosx(4cos^2x-3), якщо ctgx=5/3.
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sedinalana
Verified answer
Сtgx=5/3
sin²x=1:(1+ctg²x)=1:(1+25/9)=9/34
sinx=3/√34
cos²x=1-sin²x=1-9/34=25/34
cosx=5/√34
sinx(3-4sin²x)/cosx(4cos²x-3)=3/√34*(3-18/17):5√34*(50/17-3)=
=3/√34*33/17:5/√34*(-1/17)=-99/17√34*17√34=-99
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Answers & Comments
Verified answer
Сtgx=5/3sin²x=1:(1+ctg²x)=1:(1+25/9)=9/34
sinx=3/√34
cos²x=1-sin²x=1-9/34=25/34
cosx=5/√34
sinx(3-4sin²x)/cosx(4cos²x-3)=3/√34*(3-18/17):5√34*(50/17-3)=
=3/√34*33/17:5/√34*(-1/17)=-99/17√34*17√34=-99