F.3 trigonometric identities 5條

billyconan

我又唔識做la ~help

YSC

懶打  x先當成  fita  吧

1/( cos x *sin(90-x))  -  tanx / tan(90-x)

= 1/ cos ^2 (x)  - tan^2 (x)   PS: sin(90-x)=cosx  and tan(90-x)= 1/tanx

= (1 - sin^2 x)  /  cos ^2 x   PS: tan x = sinx/cosx
= cos^2  x /  cos^2  x
=1

YSC

sin 32 = cos (66 - x/2)

cos (90-32) = cos(66- x/2)

58 = 66 - x/2
x/2 = 8
x = 16

YSC

tan (x +45)  = 1/ tan(x/4)

tan(x+45) = tan (90- x/4)

x+45 = 90- x/4

5x/4 = 45
x = 9 *4 = 36

YSC

tan (x + 15) = 1/ tan (x+60)

tan (x+15) = tan(90- x - 60)
x +15 = 30 - x

2x = 15
x = 7.5

YSC

1/cos(90-x)   -   cos(90-x)tan(90-x)/ tanx

=1/ sin x  -  sinx / tan^2 x       PS: 1/tanx =  cosx/ sinx

=1/sinx - sinx * cos^2  x / sin^2   x

= 1/ sinx  - cos^2  x / sinx

= (1- cos^2 x)   / sinx

= sin ^2 x / sinx

= sinx