Trigonometric Identities

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Trigonometric Identities
1. Show that
tan x cos x = sin x
2. Show that
sin x
= cos x
tan x
3. Show that
tan x
1
=
sin x
cos x
4. Show that
sin 2 x
= sin x cos x
tan x
1 - cos 2 A
5. Show that
= tan 2 A
2
cos A
6. Show that
1 - sin 2 A
= 1
cos 2 A
7. Show that (cos x + sin x)2 = 1 + 2sin x cos x
8. Show that (cos x + sin x)(cos x – sin x) + 2sin2 x = 1
9. Show that sin3 x + sin x cos2 x = sin x
10. Show that
cos2 x sin2 x + cos4 x = cos2 x
11. Show that
sin x
= tan x
cos x + cos x sin 2 x
12. Show that
tan2 x cos2 x = 1 – cos2 x
13. If sin x =
3
5
14. If sin x =
5
13
and cos x =
12
13
show that tan x =
15. If sin x =
24
25
and cos x =
7
25
show that tan x =
3
and cos x =
4
5
show that tan x =
3
4
5
12
24
7
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