√2sin(x/2+π/4)cos(x/2)=√2/2sin(x+π/4)+ 1/2 怎么得到的

已知sin[a-b]cos a-cos[b-a]sin a=3/5,b是第三象限角,求sin[b+5π/4]的值第一题1/2cos x-√3/2sin x第二题√3sin x+cos x第三题√2[sin x-cos x]第四题√2cos x-√6sin x 化简sin^4x-sin^2x+cos^2x 化简:sin^4 x-sin^2 x+cos^2 x 化简sin^4x+cos^2x 化简(sin^2x-cos^4x+cos^2x-sin^4x)/(sin^2x-cos^6x+cos^2x-sin^6x) 求证:(sin 2x /(1-cos 2x) )·(sin x /(1+sin x))=tan (π/4-x/2). 证明sin^4x-cos^4x=sin^2x-cos^2x 求证sin^4x-cos^4x=sin^2x-cos^2x 证明sin^2(x)+cos^2(x+30)+sin(x)cos(x+30)=3/4 用cos x表示sin^4 x -sin^2 x +cos^2 x 用cos x表示sin^4x-sin^2 x+cos^2 x 化简[1-(sin^4x-sin^2cos^2x+cos^4x)/(sin^2)]+3sin^2x 化简sin(3π-x)cos(x-3/2)cos(4π-x)/tan(x-5π)cos(π/2+x)sin(x-5/2π) 化简sin(3π-x)cos(x-3/2)cos(4π-x)/tan(x-5π)cos(π/2+x)sin(x-5/2π) 求证（cos^2 x-sin^2 x)(cos^4 x+sin^4 x)+1/4 sin 2x sin 4x=cos 2x 化简1+sin x/cos x·sin2x/2cos²（π/4-x/2） y=4√2sin x cos x+cos 2x 的值域是 化简f(x)=(1-√2*cos(2x-π/4))/sin(π/2-x)