Question

1.已知a是第三象限角,化简√((1+sin a)/(1-sin a))-√((1-sin a)/(1+sin a))为

Answer 1

1.√((1+sin a)/(1-sin a))=[√(1-sin²a)]/(1-sin a)=-cos a/(1-sin a) ①

同理

√((1-sin a)/(1+sin a))=-cos a/(1+sin a) ②

①+②得

-cos a/(1-sin a)-cos a/(1+sin a)=-2tan a

选 A

2.lg (1+cos A)=m,lg 1/(1-cos A)=n

m-n=lg (1+cos A)-lg 1/(1-cos A)=lg(1-cos²A)=2lg sinA

lg sinA=(m-n)/2

选 D