`c)(1-cosa)(1+cosa)=1-cosa^2=sin^2a+cos^2a-cos^2a=sin^2a` $\\$ `d)1+sin^2a+cos^2a=1+1=2` $\\$ `e)sinB-sinBcos^2B=sinB(1-cos^2B)=sinB(cos^2B+sin^2B-cos^2B)=sinB.sin^2B=sinB^3` $\\$ `f)tg^2a-sin^2atg^2a=tg^2a(1-sin^2a)=tg^2(cos^2a+sin^2a-sin^2a)=tg^2a.cos^2a` $\\$ `h)tg^2a(2cos^2a+sin^2a-1)=tg^2a(2cos^2a+sin^2a-sin^2a-cos^2a)=tg^2a.cos^2a` $\\$ `i)sin^2 12^@+sin^2 22^@+sin^2 32^@+sin^2 58^@+sin^2 68^@+sin^2 78^@=(sin^2 12^@+sin^2 78^@)+(sin^2 22^@+sin^2 68^@)+(sin^2 32^@+sin^2 58^@)=1+1+1=3`
