a: \(VT=\dfrac{\left(sina+cosa\right)^3-3\cdot sina\cdot cosa\left(sina+cosa\right)}{sina+cosa}\)

=(sina+cosa)^2-3*sina*cosa

=sin^2a+cos^2a-sina*cosa

=1-sina*cosa=VP

c: VT=(sin^2a+cos^2a)^2-2*sin^2a*cos^2a-(sin^2a+cos^2a)^3+3*sin^2a*cos^2a*(sin^2a+cos^2a)

=1-2sin^2a*cos^2a-1+3*sin^2a*cos^2a

=sin^2a*cos^2a=VP

a: (sina+cosa)^2

=sin^2a+cos^2a+2*sina*cosa

=1+sin2a

b: \(cos^4a-sin^4a=\left(cos^2a-sin^2a\right)\left(cos^2a+sin^2a\right)\)

\(=cos^2a-sin^2a=cos2a\)

A = 2 ( sin 2 α   +   cos 2 α ) ( sin 4 α   +   cos 4 α   -   sin 2 α cos 2 α )

-   3 ( sin 4 α   +   cos 4 α )

     =   - sin 4 α   -   cos 4 α   -   2 sin 2 α cos 2 α

        =   - ( sin ² α   +   cos ² α ) 2   =   - 1

c: 2(sin^6a+cos^6a)+1

=2[(sin^2a+cos^2a)^3-3*sin^2a*cos^2a]+1

=2-6sin^2acos^2a+1

=3-6*sin^2a*cos^2a

=3(sin^4a+cos^4a)

a:

Sửa đề: =-tana*tanb

 \(VT=\left(\dfrac{sina}{cosa}-\dfrac{sinb}{cosb}\right):\left(\dfrac{cosa}{sina}-\dfrac{cosb}{sinb}\right)\)

\(=\dfrac{sina\cdot cosb-sinb\cdot cosa}{cosa\cdot cosb}:\dfrac{cosa\cdot sinb-cosb\cdot sina}{sina\cdot sinb}\)

\(=\dfrac{sin\left(a-b\right)}{cosa\cdot cosb}\cdot\dfrac{sina\cdot sinb}{sin\left(b-a\right)}\)

\(=-tana\cdot tanb\)

=VP

a: \(A=cos^4a+2\cdot cos^2a\cdot\sin^2a+\sin^4a\)

\(=\left(cos^2a+\sin^2a\right)^2=1^2\)

=1

=>A không phụ thuộc vào biến

b: \(B=\sin^4a+cos^2a\cdot\sin^2a+cos^2a\)

\(=\sin^2a\left(\sin^2a+cos^2a\right)+cos^2a\)

\(=\sin^2a+cos^2a\)

=1

=>B không phụ thuộc vào biến

c: \(C=2\left(\sin a-cosa\right)^2-\left(\sin a+cosa\right)^2+6\cdot\sin a\cdot cosa\)

\(=2\left(1-2\cdot\sin a\cdot cosa\right)-\left(1+2\cdot\sin a\cdot cosa\right)+6\cdot\sin a\cdot cosa\)

\(=2-4\cdot\sin a\cdot cosa-1-2\cdot\sin a\cdot cosa+6\cdot\sin a\cdot cosa\)

=2-1

=1

=>C không phụ thuộc vào biến

d: \(D=\left(\tan a-\cot a\right)^2-\left(\tan a+\cot a\right)^2\)

\(=\tan^2a-2\cdot\tan a\cdot\cot a+\cot^2a-\left(\tan^2a+2\cdot\tan a\cdot\cot a+\cot^2a\right)\)

\(=-4\cdot\tan a\cdot\cot a=-4\)

=>D không phụ thuộc vào biến

e: \(E=4\cdot cos^2a+\left(\sin a-cosa\right)^2+\left(\sin a+cosa\right)^2+2\left(\sin^2a-cos^2a\right)\)

\(=4\cdot cos^2a+\sin^2a+cos^2a-2\cdot\sin a\cdot cosa+\sin^2a+cos^2a+2\cdot\sin a\cdot cosa+2\left(\sin^2a-cos^2a\right)\)

\(=4\cdot cos^2a+2\cdot\sin^2a-2\cdot cos^2a+2\)

\(=2\cdot\sin^2a+2\cdot cos^2a+2=2+2=4\)

=>E không phụ thuộc vào biến

f: \(F=\frac{1}{1+\sin a}+\frac{1}{1-\sin a}-2\cdot\tan^2a\)

\(=\frac{1-\sin a+1+\sin a}{\left(1+\sin a\right)\left(1-\sin a\right)}-2\cdot\tan^2a\)

\(=\frac{2}{1-\sin^2a}-2\cdot\tan^2a=\frac{2}{cos^2a}-2\cdot\frac{\sin^2a}{cos^2a}=\frac{2\cdot\left(1-\sin^2a\right)}{cos^2a}=2\)

=>F không phụ thuộc vào biến

cos^4a-sin^4a

=(cos^2a-sin^2a)(cos^2a+sin^2a)

=cos^2a-sin^2a

=cos2a

j vậy trời, mik báo cáo đấy;-;

bạn có trả lời nhầm bài khum thế, nếu bạn bt làm thì giúp mik iii, plss

a: \(1-\sin^2\alpha=cos^2\alpha\)

b: \(\left(1-cos\alpha\right)\left(1+cos\alpha\right)=1-cos^2\alpha=\sin^2\alpha\)

c: \(1+\sin^2\alpha+cos^2\alpha=1+1=2\)

d: \(\sin^4\alpha+cos^4\alpha+2\cdot\sin^2\alpha\cdot cos^2\alpha\)

\(=\left(\sin^2\alpha+cos^2\alpha\right)^2\)

=1^2=1

e: \(\tan^2\alpha-\sin^2\alpha\cdot\tan^2\alpha\)

\(=\tan^2\alpha\left(1-\sin^2\alpha\right)=\tan^2\alpha\cdot cos^2\alpha=\sin^2\alpha\)

a: \(Q=\sin^6a+cos^6a+3\cdot\sin^2a\cdot cos^2a\)

\(=\left(\sin^2a+cos^2a\right)^3-3\cdot sin^2a\cdot cos^2a\cdot\left(\sin^2a+cos^2a\right)+3\cdot\sin^2a\cdot cos^2a\)

\(=1-3\cdot\sin^2a\cdot cos^2a+3\cdot\sin^2a\cdot cos^2a\)

=1