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a) khai triển được 2sin2+2cos2=2(sin2+cos2=2.1=2
b)cot2-cos2.cot2=cot2(1-cos2)=cot2.sin2=cos2/sin2.sin2=cos2
c)sin.cos(tan+cot)=sin.cos.tan+sin.cos.cot=sin.cos.sin/cos+sin.cos.cos/sin=sin2+cos2=1
d)tan2-tan2.sin2=tan2(1-sin2)=tan2.cos2=sin2/cos2.cos2=sin2
Cái này mình vừa làm ban nãy rồi mà-.-
Ta có: \(2\sin^2\alpha+\cot^2\alpha\cdot\sin^2\alpha+\cos^2\alpha\)
\(=\left(\sin^2\alpha+\cos^2\alpha\right)+\left(\sin^2\alpha+\frac{\cos^2\alpha}{\sin^2\alpha}\cdot\sin^2\alpha\right)\)
\(=1+\left(\sin^2\alpha+\cos^2\alpha\right)\)
\(=1+1=2\)
\(B=\left(1+\dfrac{sin^2a}{cos^2a}\right).cos^2a-\left(1+\dfrac{cos^2a}{sin^2a}\right).sin^2a\)
\(=\dfrac{\left(sin^2a+cos^2a\right)}{cos^2a}.cos^2a-\left(\dfrac{sin^2a+cos^2a}{sin^2a}\right).sin^2a\)
\(=1-1=0\)
Bài làm:
Ta có: \(2\sin^2\alpha+\cot^2\alpha.\sin^2\alpha+\cos^2\alpha\)
\(=\left(\sin^2\alpha+\cos^2\alpha\right)+\frac{\cos^2\alpha}{\sin^2\alpha}\cdot\sin^2\alpha+\sin^2\alpha\)
\(=1+\cos^2\alpha+\sin^2\alpha\)
\(=1+1=2\)
a)
\(A=\cot^2x\left(\cos^2x-1+\sin^2x\right)+\sin^2x\)
\(A=\cot^2x\left(\cos^2x+\sin^2x-1\right)+\sin^2x\)
\(A=\cot^2x\left(1-1\right)+\sin^2x\)
\(A=\cot^2x.0+\sin^2x\)
\(A=\sin^2x\)
b) \(B=\cos^4\alpha-\sin^4\alpha+2\sin^2\alpha+8\)
\(B=\left(cos^2\alpha+sin^2\alpha\right)\left(cos^2\alpha-sin^2\alpha\right)+2\sin^2\alpha+8\)
\(B=cos^2\alpha-sin^2\alpha+2\sin^2\alpha+8\)
\(B=cos^2\alpha+sin^2\alpha+8\)
\(B=1+8\)
\(B=9\)
Đặt \(\sin^2\alpha=x\Rightarrow\cos^2\alpha=1-\sin^2\alpha\)
\(A=x^3+\left(1-x\right)^3+3x-\left(1-x\right)=x^3+1-3x+3x^2-x^3+3x-1+x=3x^2+x\)
Vậy \(A=3\sin^4\alpha+\sin^2\alpha\). NHỚ NHA!
`D=(sin^2 alpha + 2sin alpha . cos alpha + cos^2 alpha - sin^2 alpha + 2 sin alpha . cos alpha + cos^2 alpha ) / (sin alpha . cos alpha )`
`D=(4 sin alpha . cos alpha )/(sin alpha . cos alpha )`
`D=4`
`D=(sin^2 alpha + 2sin alpha . cos alpha + cos^2 alpha - (sin^2 alpha - 2 sin alpha . cos alpha + cos^2 alpha )) / (sin alpha . cos alpha )`
`D=(sin^2 alpha + 2sin alpha . cos alpha + cos^2 alpha - sin^2 alpha + 2 sin alpha . cos alpha - cos^2 alpha ) / (sin alpha . cos alpha )`
`D=((sin^2 alpha - sin^2 alpha ) + (2sin alpha . cos alpha + cos^2 alpha + 2 sin alpha . cos alpha) +( cos^2 alpha - cos^2 alpha )) / (sin alpha . cos alpha )`
`D=(4 sin alpha . cos alpha )/(sin alpha . cos alpha )`
`D=4`
\(A=sin^2a+cos^2a+\left(tana\cdot cota\right)^2\)
\(=1+1^2\)
\(=1+1=2\)