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Problemas populares Trigonometría

verificar sin(2x)+sin(x)=0	`prove` sin(2`x`)+sin(`x`)=0
verificar (cot(θ))/(csc(θ))=cot(θ)csc(θ)	`prove` cot(θ)csc(θ) =cot(θ)csc(θ)
verificar 1=cos(x)csc(x)tan(x)	`prove` 1=cos(`x`)csc(`x`)tan(`x`)
verificar csc^2(x)+sec^2(x)=1	`prove` csc²(`x`)+sec²(`x`)=1
verificar 3-3cos^2(x)+4-4sin^2(x)=3+cos^2(x)	`prove` 3−3cos²(`x`)+4−4sin²(`x`)=3+cos²(`x`)
verificar-(1+cot^2(x))=-csc^2(x)	`prove` −(1+cot²(`x`))=−csc²(`x`)
verificar (sin(a)+tan(a))/(1+cos(a))=tan(a)	`prove` sin(`a`)+tan(`a`)1+cos(`a`) =tan(`a`)
verificar (4sec(x)-4)/(1-cos(θ))=4sec(x)	`prove` 4sec(`x`)−41−cos(θ) =4sec(`x`)
verificar 1+cot^2(x)=(tan^2(x)+1)/(tan^2(x))	`prove` 1+cot²(`x`)=tan²(`x`)+1tan²(`x`)
verificar sin(180+θ)=-sin(θ)	`prove` sin(180^◦+θ)=−sin(θ)
verificar (1-tan^2(x))/(1+tan^2(x))=sec(x)	`prove` 1−tan²(`x`)1+tan²(`x`) =sec(`x`)
verificar 2sec(x)=2+2tan(x)	`prove` 2sec(`x`)=2+2tan(`x`)
verificar sin^2(θ)(1+cos^2(θ))=1	`prove` sin²(θ)(1+cos²(θ))=1
verificar sin(x)tan(x)=cos(x)	`prove` sin(`x`)tan(`x`)=cos(`x`)
verificar 2sin^2(x/2)+4cos^2(x/2)-3=cos(x)	`prove` 2sin²(`x`2 )+4cos²(`x`2 )−3=cos(`x`)
verificar tan(2u)=((2tan(u)))/(1-tan^2(u))	`prove` tan(2`u`)=(2tan(`u`))1−tan²(`u`)
verificar 1/(-sin(x))=sec(x)tan(x)	`prove` 1−sin(`x`) =sec(`x`)tan(`x`)
verificar 6cos(θ)=6cos(-θ)	`prove` 6cos(θ)=6cos(−θ)
verificar ((tan(2x)+cot(2x)))/(csc(2x))=sec(2x)	`prove` (tan(2`x`)+cot(2`x`))csc(2`x`) =sec(2`x`)
verificar (cos(θ)-sin(θ))^2=1	`prove` (cos(θ)−sin(θ))²=1
verificar cos(x)=1=cos(0)=1	`prove` cos(`x`)=1=cos(0)=1
verificar (tan(x)+1)(tan(x)-1)=sec^2(x)-2	`prove` (tan(`x`)+1)(tan(`x`)−1)=sec²(`x`)−2
verificar 1/(csc(x)+1)= 1/(sin(x)+1)	`prove` 1csc(`x`)+1 =1sin(`x`)+1
verificar tan(θ)+1=(sin(θ))/(cos(θ))+1	`prove` tan(θ)+1=sin(θ)cos(θ) +1
verificar (1+tan^2(α))cos^2(α)=1	`prove` (1+tan²(α))cos²(α)=1
verificar 1/(sin^2(x))= 1/(csc^2(x))	`prove` 1sin²(`x`) =1csc²(`x`)
verificar sin(x)(1+tan^2(x))=sin(x)sec^2(x)	`prove` sin(`x`)(1+tan²(`x`))=sin(`x`)sec²(`x`)
verificar (tan^2(X))/(1+cot^2(X))=sin^4(X)	`prove` tan²(`X`)1+cot²(`X`) =sin⁴(`X`)
verificar sin(x)+cot(x)cos(x)= 1/(sin(x))	`prove` sin(`x`)+cot(`x`)cos(`x`)=1sin(`x`)
verificar 1+cos(6x)=2cos^2(3x)	`prove` 1+cos(6`x`)=2cos²(3`x`)
verificar (sec(a))/(cot(a)+tan(a))=sin(a)	`prove` sec(`a`)cot(`a`)+tan(`a`) =sin(`a`)
verificar (4+2sin(θ))/(1-sin(θ))=3	`prove` 4+2sin(θ)1−sin(θ) =3
verificar (sin(4x))/4 =4(sin(x)cos(x))/4	`prove` sin(4`x`)4 =4sin(`x`)cos(`x`)4
verificar (sin^2(x))/(1-sin^2(x))=tan^2(x)	`prove` sin²(`x`)1−sin²(`x`) =tan²(`x`)
verificar sin(-30)=-sin(30)	`prove` sin(−30^◦)=−sin(30^◦)
verificar cos(1/2 pi-x)=sin(x)	`prove` cos(12 π−`x`)=sin(`x`)
verificar sin(x)-cos(x)+1=cos(x)	`prove` sin(`x`)−cos(`x`)+1=cos(`x`)
verificar cos(12x)=1-2sin^2(6x)	`prove` cos(12`x`)=1−2sin²(6`x`)
verificar tan(θ)=tan(pi+θ)	`prove` tan(θ)=tan(π+θ)
verificar cos(x)-cos^3(x)=cos(x)-sin^2(x)	`prove` cos(`x`)−cos³(`x`)=cos(`x`)−sin²(`x`)
verificar cos(B)csc(B)tan(B)=11	`prove` cos(`B`)csc(`B`)tan(`B`)=11
verificar tan(8x)=(8tan(x))/(1-tan^2(x))	`prove` tan(8`x`)=8tan(`x`)1−tan²(`x`)
verificar tan(-a)=(cos(pi/2+a))/(cos(a))	`prove` tan(−`a`)=cos(π2 +`a`)cos(`a`)
verificar sin(θ)-1/(sin(θ))=cos(θ)	`prove` sin(θ)−1sin(θ) =cos(θ)
verificar cos^8(x)=sin^7(x)cos^1(x)	`prove` cos⁸(`x`)=sin⁷(`x`)cos¹(`x`)
verificar (cot(x)+1)^2-2cot(x)=csc^2(x)	`prove` (cot(`x`)+1)²−2cot(`x`)=csc²(`x`)
verificar cos(θ)= 1/3	`prove` cos(θ)=13
verificar sec(θ)-(tan(θ))/(csc(θ))=cos(θ)	`prove` sec(θ)−tan(θ)csc(θ) =cos(θ)
verificar sec^2(x)=(1+tan^2(x))	`prove` sec²(`x`)=(1+tan²(`x`))
verificar cot^2(x)sec^2(x)=cot^2(x)+1	`prove` cot²(`x`)sec²(`x`)=cot²(`x`)+1
verificar (sin(x))/(cos(x)+sin(x))=1	`prove` sin(`x`)cos(`x`)+sin(`x`) =1
verificar cos(x)=(cot(x))/(tan(x))	`prove` cos(`x`)=cot(`x`)tan(`x`)
verificar cos^2(2a)-sin^2(2a)=cos(4a)	`prove` cos²(2`a`)−sin²(2`a`)=cos(4`a`)
verificar tan(2x)-2cos(x)=0	`prove` tan(2`x`)−2cos(`x`)=0
verificar cos^2(a)cot^2(a)=cot^2(a)-cos^2(a)	`prove` cos²(`a`)cot²(`a`)=cot²(`a`)−cos²(`a`)
verificar cos(θ)= 1/2	`prove` cos(θ)=12
verificar csc(2x)= 1/(sin^2(x)-1)	`prove` csc(2`x`)=1sin²(`x`)−1
verificar (1+tan^2(α))(1-sin^2(α))=1	`prove` (1+tan²(α))(1−sin²(α))=1
verificar csc(θ)-cot(θ)=(1-cos(θ))/(sin(θ))	`prove` csc(θ)−cot(θ)=1−cos(θ)sin(θ)
verificar tan(x)=tan(x)+2sin^2(x)	`prove` tan(`x`)=tan(`x`)+2sin²(`x`)
verificar 1/(2cot(1-cos^2(x)))=csc(2x)	`prove` 12cot(1−cos²(`x`)) =csc(2`x`)
verificar cot(u)= 1/(tan(u))	`prove` cot(`u`)=1tan(`u`)
verificar-sin(2x)=-4cos(x)sin(x)	`prove` −sin(2`x`)=−4cos(`x`)sin(`x`)
verificar cos(θ)(tan(θ)-sec(-θ))=sin(θ)-1	`prove` cos(θ)(tan(θ)−sec(−θ))=sin(θ)−1
verificar cos(pi/2)=-0	`prove` cos(π2 )=−0
verificar cos(x)+1=sin(2x)	`prove` cos(`x`)+1=sin(2`x`)
verificar ((sec^2(x)))/(sec^2(x)-1)=csc^2(x)	`prove` (sec²(`x`))sec²(`x`)−1 =csc²(`x`)
verificar (sin(x))(tan(x)cos(x)-cot(x)cos(x))=1-2cos(2x)	`prove` (sin(`x`))(tan(`x`)cos(`x`)−cot(`x`)cos(`x`))=1−2cos(2`x`)
verificar sin(20)=2cos(10)*sin(10)	`prove` sin(20^◦)=2cos(10^◦)· sin(10^◦)
verificar sin^2(x)=sec(x)cos(x)-cos^2(x)	`prove` sin²(`x`)=sec(`x`)cos(`x`)−cos²(`x`)
verificar 1-2sin^2(2θ)=8cos^4(θ)-8cos^2(θ)+1	`prove` 1−2sin²(2θ)=8cos⁴(θ)−8cos²(θ)+1
verificar sech^2(x)+tanh^2(x)=1	`prove` sech²(`x`)+tanh²(`x`)=1
verificar 2cos^2(A)-cos(2A)-1=0	`prove` 2cos²(`A`)−cos(2`A`)−1=0
verificar (cot(x)+1)/(cos(x)+sin(x))=csc(x)	`prove` cot(`x`)+1cos(`x`)+sin(`x`) =csc(`x`)
verificar csc(A)= 7/4	`prove` csc(`A`)=74
verificar (sin^2(x))/(sin^2(x))=sin(x)	`prove` sin²(`x`)sin²(`x`) =sin(`x`)
verificar csc(cos(+sin(x)))=cot(+1)	`prove` csc(cos(+sin(`x`)))=cot(+1)
verificar 4sin(x/2)cos(x/2)=2sin(x)	`prove` 4sin(`x`2 )cos(`x`2 )=2sin(`x`)
verificar 5cos(x)-3=3cos(x)-4	`prove` 5cos(`x`)−3=3cos(`x`)−4
verificar (cos(φ)+1)/(sin(φ)+tan(φ))=cot(φ)	`prove` cos(φ)+1sin(φ)+tan(φ) =cot(φ)
verificar tan(x)+tan(x)=0	`prove` tan(`x`)+tan(`x`)=0
verificar 2cos^2(x)-cos(2x)=1	`prove` 2cos²(`x`)−cos(2`x`)=1
verificar-cot^2(x)=1-csc^2(x)	`prove` −cot²(`x`)=1−csc²(`x`)
verificar 1/(tan(2θ))=(cot^2(θ)-1)/(2cot(θ))	`prove` 1tan(2θ) =cot²(θ)−12cot(θ)
verificar (1-cos(θ))+sin^2(θ)=2	`prove` (1−cos(θ))+sin²(θ)=2
verificar 1/(sec(θ))=(sec(θ))^{-1}	`prove` 1sec(θ) =(sec(θ))⁻¹
verificar sin(2θ)+cos(2θ)=1	`prove` sin(2θ)+cos(2θ)=1
verificar 25(sec^2(5x)-tan^2(5x))=25	`prove` 25(sec²(5`x`)−tan²(5`x`))=25
verificar cot^2(x)=((cos^2(x)))/(1-cos^2(x))	`prove` cot²(`x`)=(cos²(`x`))1−cos²(`x`)
verificar+(cos(x))/(1-sin(x))=sec(x)+tan(x)	`prove` +cos(`x`)1−sin(`x`) =sec(`x`)+tan(`x`)
verificar sin((4pi)/3)=sqrt(3)cos((2pi)/3)	`prove` sin(4π3 )=√3cos(2π3 )
verificar sin^2(x)+sin^2(θ)=1	`prove` sin²(`x`)+sin²(θ)=1
verificar (cot(x)-sec(x))/(csc(x))=1	`prove` cot(`x`)−sec(`x`)csc(`x`) =1
verificar 1+tan^2(x)+cot(x)=sec^2(x)+cos(x)	`prove` 1+tan²(`x`)+cot(`x`)=sec²(`x`)+cos(`x`)
verificar cos(θ)sec(θ)=tan(θ)cot(θ)	`prove` cos(θ)sec(θ)=tan(θ)cot(θ)
verificar cos(x)-cos(x)=2cos(x)	`prove` cos(`x`)−cos(`x`)=2cos(`x`)
verificar (cos^2(2θ))/2 =(1+cos(4θ))/8	`prove` cos²(2θ)2 =1+cos(4θ)8
verificar (cos^2(x))/(sin^2(x))+1=csc^2(x)	`prove` cos²(`x`)sin²(`x`) +1=csc²(`x`)
verificar cot(x)-cot(x)cos^2(x)=sin(x)cos(x)	`prove` cot(`x`)−cot(`x`)cos²(`x`)=sin(`x`)cos(`x`)
verificar 1/(sec(θ))=arcsec(θ)	`prove` 1sec(θ) =arcsec(θ)

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