Question

  Chứng minh các đẳng thức

Answer 1

e: \(2\cdot cos^4x-sin^4x+sin^2x\cdot cos^2x+3\cdot sin^2x\)

\(=\left(cos^4x-sin^4x\right)+cos^4x+sin^2x\cdot cos^2x+3\cdot sin^2x\)

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

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

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

=>ĐPCM

f: \(\left(cotx+tanx\right)^2-\left(cotx-tanx\right)^2\)

\(=\left(cotx+tanx-cotx+tanx\right)\left(cotx+tanx+cotx-tanx\right)\)

\(=2\cdot tanx\cdot2\cdot cotx=2\cdot2=4\)