已知tan²a=2tan²B+1,求证sin²+2sin²a-1

问题描述:

已知tan²a=2tan²B+1,求证sin²+2sin²a-1

sin²a/cos²a=2sin²b/cos²b+1
sin²acos²b=2sin²bcos²a+cos²acos²b
sin²a(1-sin²b)=2sin²b(1-sin²a)+(1-sin²a)(1-sin²b)
sin²a-sin²asin²b=2sin²b-2sin²bsin²a+1-sin²a-sin²b+sin²asin²b
2sin²a=sin²b+1
sin²b=sin²a-1