幫幫我 maths~1

13)1/[1+(tanx)^2]+(sinx)^2
= 1/(secx)^2+ (sinx)^2
= (cosx)^2+(sinx)^2
= 1

14)sinx/(1+cosx)+ sinx/(1-cosx)
= [sin(1-cosx)+ sinx(1+cosx)]/(1+cosx)(1-cosx)
= 2sinx/1-(cosx)^2
=2sinx/(sinx)^2
= 2/sinx

15)(3cosx-2sinx)/(2cosx-3sinx)
=(3-2tanx)/(2-3tanx) .........全式除cosx
= [3-2(1/2)]/[2-3(1/2)]
= 2/(1/2)
= 4

16a) (sinx-3cosx)/(cosx-3sinx)=9/5
5(sinx-3cosx)=9(cosx-3sinx)
5sinx-15cosx= 9cosx-27sinx
32sinx= 24 cosx
tanx = 24/32
tanx = 3/4

16b) sinx =3/5
cosx =4/5
3sinx+4cosx
= 3(3/5)+4(4/5)
=9/5+16/5
=5

13.1/[1+(tanx)^2]+(sinx)^2
= 1/(secx)^2+ (sinx)^2
= (cosx)^2+(sinx)^2
= 1

14.sinx/(1+cosx)+ sinx/(1-cosx)
= [sin(1-cosx)+ sinx(1+cosx)]/(1+cosx)(1-cosx)
= 2sinx/1-(cosx)^2
=2sinx/(sinx)^2
= 2/sinx

15.(3cosx-2sinx)/(2cosx-3sinx)
=(3-2tanx)/(2-3tanx) .........全式除cosx
= [3-2(1/2)]/[2-3(1/2)]
= 2/(1/2)
= 4

16a.(sinx-3cosx)/(cosx-3sinx)=9/5
5(sinx-3cosx)=9(cosx-3sinx)
5sinx-15cosx= 9cosx-27sinx
32sinx= 24 cosx
tanx = 24/32
tanx = 3/4

16b. sinx =3/5
cosx =4/5
3sinx+4cosx
= 3(3/5)+4(4/5)
=9/5+16/5
=5