sin  α  - sin  α   c o s 2 α  = sin  α (1 – c o s 2 α )

= sin  α [( sin 2 α  +  c o s 2 α ) –  c o s 2 α ]

= sin  α .( sin 2 α  +  c o s 2 α  –  c o s 2 α )

= sin  α . sin 2 α  =  sin 3 α

(1 - cos  α )(1 + cos  α ) = 1 –  c o s 2 α  = ( sin 2 α  +  c o s 2 α ) –  c o s 2 α

= sin 2 α  +  c o s 2 α  –  c o s 2 α  =  sin 2 α

Chọn D 

D

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

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

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

\(=1\)

\(\sin^4\alpha+\cos^4\alpha+2\sin^2\alpha.\cos^2\alpha=\left(\sin^2\alpha+\cos^2\alpha\right)^2=1\)

\(\tan^2\alpha\left(2.\cos^2\alpha+\sin^2\alpha-1\right)=\tan^2\alpha\left(\cos^2\alpha+\left(\sin^2\alpha+\cos^2\alpha\right)-1\right)\)\(=\tan^2\alpha.\cos^2\alpha=\left(\frac{1}{\cos^2\alpha}-1\right)\cos^2\alpha=1-\cos^2\alpha=\sin^2\alpha\)

\(A=sin\alpha-sin\alpha\cdot cos^2\alpha\)

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

\(A=sin\alpha\cdot sin^2\alpha\)

\(A=sin^3\alpha\)

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Thay vào biểu thức A ta được: A=2sin α .

Chọn A.

sin a - sin a. cos²a = sin a (1- cos²a) = sin a . sin²a = sin³a

\(\sin a-\sin a.\cos^2a\)

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

=\(\sin a.sin^2a\)

=\(sin^3a\)

\(A=\cos\left(\text{π}-\dfrac{x}{2}\right)-\sin\left(\text{π}-x\right)\)

\(=\sin x+\sin x=2\cdot\sin x\)

\(B=\cos\left(2\text{π}+\dfrac{\text{π}}{2}-x\right)+\sin\left(4\text{π}+\dfrac{\text{π}}{2}-x\right)-\cos\left(6\text{π}+\dfrac{3}{2}\text{π}+x\right)-\sin\left(16\text{π}+\dfrac{3}{2}\text{π}+x\right)\)

\(=\sin x+\cos x-\cos\left(\dfrac{3}{2}\text{π}+x\right)-\sin\left(\dfrac{3}{2}\text{π}+x\right)\)

\(=\sin x+\cos x-\cos\left(\text{π}+\dfrac{\text{π}}{2}+x\right)-\sin\left(\text{π}+\dfrac{\text{π}}{2}+x\right)\)

\(=\cos x+\sin x+\cos\left(\dfrac{1}{2}\text{π}+x\right)+\sin\left(\dfrac{1}{2}\text{π}+x\right)\)

\(=\cos x+\sin x-\sin x+\cos x=2\cos x\)