F.2 maths(Trigonometric relations)

The following are trigonometric identities
sin^x + cos^x = 1
tanx = sinx / cosx

1)
1/sin* - cos^x/sinx
= (1 - cos^x) / sinx
= sin^x / sinx
= sinx

2)
1-cos^x/(sinxcosx)
= sin^x/(sinxcosx)
= sinx / cosx
= tanx

3)
If tanx = 3 and cosx = 1/√10, find the value of sinx.
tanx = sinx / cosx

sinx = tanx(cosx)
= 3(1/√10)
= 3(√10) / 10

4)
tan^xcos^x + cos^x
(since tan^x = sin^x / cos^x)

tan^xcos^x + cos^x
= (sin^x / cos^x)(cos^x) + cos^x
= sin^x + cos^x
= 1

5)
If cosx = 1/4, find the value of 5 sin^x - 3 cos^x.
(since sin^x = 1 - cos^x & cos^x = (1/4)^2 = 1/16)

5 sin^x - 3 cos^x
= 5(1 - cos^x) - 3 cos^x
= 5 - 8 cos^x
= 5 - 8 (1/16)
= 4.5 //

我將 * 變做 x 會清楚d....
1)1/sinx - cos^x/sinx
=(1-cos^x)/sinx
=sin^x/sinx
=sinx

2)1-cos^x/sinxcosx
=sin^x/sinxcosx
=sinx/cosx
=tanx

3)tanx=3
sinx/cosx=3
sinx/(1/√10)=3
sinx=3/√10

4)tan^xcos^x+cos^x
=sin^x/cos^x X cos^x+cos^x
=sin^x+cos^x
=1

5)sin^x+cos^x=1
sin^x=1-(1/4)^
=15/16

5 sin^x - 3 cos^x
=5(15/16)-3(1/16)
=72/16
=9/2