Question

数学题目：已知tan阿尔法平方=2tan贝塔平方+1,求sin贝塔平方=2sin阿尔法平方-1

Answer 1

tan^2α=2tan^2β+1

sin^2α/cos^2α=2sin^2β/cos^2β+1

去分母得：sin^2αcos^2β=2sin^2βcos^2α+cos^2αcos^2β

sin^2α(1-sin^2β)=2sin^2β(1-sin^2α)+(1-sin^2α)(1-sin^2β)

化简得：

sin^2贝塔=2sin^2阿尔法-1