Question

Rút gọn 
C =\(8\left(cos^8x-sin^8x\right)-cos6x-7cos2x\)

Answer 1

\(C=8\left(cos^8x-sin^8x\right)-cos6x-7cos2x\)

\(=8\left[\left(cos^2x\right)^4-\left(sin^2x\right)^4\right]-cos6x-7cos2x\)

\(=8\left[\left(cos^2x\right)^2+\left(sin^2x\right)^2\right]\left[\left(cos^2x\right)^2-\left(sin^2x\right)^2\right]-cos6x-7cos2x\)

\(=8\left[1\right]\left[cos^4x-sin^4x\right]-cos6x-7cos2x\)

\(=8\left[cos^4x-\left(1-cos^2x\right)^2\right]-cos6x-cos2x\)

\(=8\left[cos^4x-1+2cos^2x-cos^4x\right]-cos6x-7cos2x\)

\(=16cos^2x-8-cos6x-7cos2x\)

\(=16cos^2x-8-\left(1-2sin^23x\right)-\left(2cos^2x-1\right)\)

\(=18cos^2x-2sin^23x-1\)

\(=18cos^2x-2\left(1-cos^26x\right)-1\)

\(=20cos^2x-2cos^26x-3\)