упростить
1)5sinx -3 +5 cosx
2)7sinx -5+7cosx
3)1-sinx ctgx cosx
4) сos[tex]cos^{2}x -sin^{2}x/2cos^{2}x-1[/tex]
5)(cos2a+1)tg^{2}a-1
6)sina+cosa)^{2}-1
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упростить
1)5sinx -3 +5 cosx
2)7sinx -5+7cosx
3)1-sinx ctgx cosx
4) сos[tex]cos^{2}x -sin^{2}x/2cos^{2}x-1[/tex]
5)(cos2a+1)tg^{2}a-1
6)sina+cosa)^{2}-1
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Verified answer
1)5sinx-3+5cosx=5(sinx+cosx)-3=5(sinx+sin(π/2-x))-3=5*2sinπ/4 cos(x-π/4)-3=
=5√2cos(x-π/4)-3
2)7sinx-5+7cosx=7√2cos(x-π/4)-5
3)1-sinx ctgx cosx=1-sinx*(cosx/sinx)*cosx=1-cos²x=sin²x
4) (cos²x-sin²x) / (2cos²x-1) = cos2x / cos2x =1
5) (cos2a+1)tg²a-1=2cos²a*(sin²a / cos²a)-1=2sin²a-1= -cos2a
6)(sina+cosa)²-1=sin²a+2sina cosa+cos²a-1=2sina cosa=sin2a