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yanaberezhnaya
@yanaberezhnaya
July 2022
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Тригонометрия 14,16,18,22
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sedinalana
Verified answer
14
cos²a=1:(1+tg²a)=1:(1+16)=1/17
cosa=-1/√17
sina=√(1-cos²a)=√(1-1/17)=√(16/17)=4/√17
(2sinacosa+2cos²a)/(cos²a-sin²a)=2sina(cosa+sina)/(cosa-sina)(cosa+sina)=
=2cos/(cosa-sina)=-2/√17:(-1/√14-4/√17)=2/√17*√17/5=2/5=0,4
15
tg2a=2tga/(1-tg²a)
2tga/(1-tg²a)=2
2-2tg²a=2tga
tga=t
2t²+2t-2=0
t²+t-1=0
D=1+4=5
t1=(-1-√5)/2 U t=(-1+√5)/2 не удов усл
18
cos2a=√(1-sin²2a)=√(1-2/4)=√2/2
(1-cos2a)²/4+(1+cos2a)²/4=(1-2cos2a+cos²+2a+1+2cos2a+cos²2a)/4=
=(2+2cos²2a)/4=2(1+cos²2a)/4=1/2*(1+1/2)=1/2*3/2=3/4
22
1-2sin²a=sina
sina=t
2t²+t-1=0
D=1+8=9
t1=(-1-3)/4=-1⇒sinx=-1⇒x=-π/2+2πk,k∈z не удов усл
t2=(-1+3)/4=1/2⇒sina=1/2
a=π/6+2πk ,k∈zне удов усл
a=5π/6+2πk,k∈z
Ответ х=5π/6
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Answers & Comments
Verified answer
14cos²a=1:(1+tg²a)=1:(1+16)=1/17
cosa=-1/√17
sina=√(1-cos²a)=√(1-1/17)=√(16/17)=4/√17
(2sinacosa+2cos²a)/(cos²a-sin²a)=2sina(cosa+sina)/(cosa-sina)(cosa+sina)=
=2cos/(cosa-sina)=-2/√17:(-1/√14-4/√17)=2/√17*√17/5=2/5=0,4
15
tg2a=2tga/(1-tg²a)
2tga/(1-tg²a)=2
2-2tg²a=2tga
tga=t
2t²+2t-2=0
t²+t-1=0
D=1+4=5
t1=(-1-√5)/2 U t=(-1+√5)/2 не удов усл
18
cos2a=√(1-sin²2a)=√(1-2/4)=√2/2
(1-cos2a)²/4+(1+cos2a)²/4=(1-2cos2a+cos²+2a+1+2cos2a+cos²2a)/4=
=(2+2cos²2a)/4=2(1+cos²2a)/4=1/2*(1+1/2)=1/2*3/2=3/4
22
1-2sin²a=sina
sina=t
2t²+t-1=0
D=1+8=9
t1=(-1-3)/4=-1⇒sinx=-1⇒x=-π/2+2πk,k∈z не удов усл
t2=(-1+3)/4=1/2⇒sina=1/2
a=π/6+2πk ,k∈zне удов усл
a=5π/6+2πk,k∈z
Ответ х=5π/6