Question

已知tanα+inα=a,tanα-sinα=b,求证（a²-b²)²=16ab

Answer 1

(a^2-b^2)^2=(a+b)^2(a-b)^2=(tanα +sinα +tanα -sinα)^2(tanα +sinα -tanα +sinα)^2=(2tanα)^2(2sinα)^2=16tan^2αsin^2α16ab=16*( tanα +sinα )(tanα -sinα)=16(tan^2α -sin^2α )=16(sin^2α/co...