求证(3-sin^4 x-cos^4 x)/2cos^2 x=1+tan^2 x+sin^2 x

问题描述:

求证(3-sin^4 x-cos^4 x)/2cos^2 x=1+tan^2 x+sin^2 x

证明:3-sin^4 x-cos^4 x=1+(1-sin^4 x)+(1-cos^4 x)=1+(1-sin^2 x)(1+sin^2 x)+(1-cos^2 x)(1+cos^2 x)=1+(cos^2 x)(1+sin^2)+(sin^2 x)(1+cos^2 x)=1+cos^2 x+sin^2 x+2(sin^2 x)(cos^2 x)=2+2(sin^2 x)(cos^2 x)...