Question

已知cota=2,求sina2a cos2a tan2a的值

Answer 1

cosa/sina=cota=2
cosa=2sina
cos²a=4sin²a
因为sin²a+cos²a=1
所以sin²a=1/5

所以
sin2a=2sinacosa
=2sina(2sina)
=4sin²a
=4/5

cos2a=1-2sin²a=3/5

tana=1/cota=1/2
tan2a=2tana/(1-tan²a)=4/3

Answer 2

cota=2
sin2a=2sinacosa=2sinacosa/(sin²a+cos²a)
分子分母 同除以sin²a
=2cota/(1+cot²a)
=4/5
cos2a=cos²-sin²a=(cos²-sin²a)/(cos²+sin²a)
分子分母 同除以sin²a
=(cot²a-1)/(cot²+1)
=3/5
tan2a=sin2a/cos2a=4/3

Answer 3

sin2a=sinacosa/(sin^2a+cos^2a)
=2cota/(1+cot^2a)
=4/5
cos2a=(cos^2a-sin^2a)/(sin^2a+cos^2a)
=(cot^2a-1)/(cot^2a+1)
=3/5
tan2a=sin2a/cos2a
=4/3