4.
\(P=2cos^2x-1+5sin^2x=-3cos^2x-1+5\left(sin^2x+cos^2x\right)\)
\(=-3cos^2x+4\)
Mà \(\dfrac{1}{cos^2x}=1+tan^2x\Rightarrow cos^2x=\dfrac{1}{1+tan^2x}\)
\(\Rightarrow P=-\dfrac{3}{1+tan^2x}+4=-\dfrac{3}{1+9}+4=...\)
5.
\(\dfrac{sinx.cos^3x-cosx.sin^3x}{cos^42x-sin^42x}=\dfrac{sinx.cosx\left(cos^2x-sin^2x\right)}{\left(cos^22x-sin^22x\right)\left(cos^22x+sin^22x\right)}\)
\(=\dfrac{\dfrac{1}{2}sin2x.cos2x}{cos^22x-sin^22x}=\dfrac{2sin2x.cos2x}{4cos4x}=\dfrac{sin4x}{4cos4x}=\dfrac{1}{4}tan4x\)
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