College Algebra & Trigonometry, 2018a

458 CHAPTER 10. TRIGONOMETRIC IDENTITIES AND EQUATIONS
Exercises 10.2
In each problem verify the given trigonometric identity.
1.
2sinx cos x
cos 2 x−sin 2 x =tan(2x) 2. sec(2x) = sec2 x
2−sec 2 x
3. sin(2x) csc x =2cosx 4.
2cosx
sin(2x) = csc x
5.
cos(2x)
x
sin x
+sinx =cot
sec x
6.
sin x+sin(2x)
sec x+2
=sinx cos x
7. (sin x +cosx) 2 =1+sin(2x) 8. (sin 2 x − 1) 2 =sin 4 x +cos(2x)
9. 2cosx− cos(2x)
cos x = sec x 10. 1+cos(2x)
1−cos(2x) =cot2 x
11.
cos(2x)
sin 2 x =cot2 x − 1 12.
cos(2x)
sin 2 x = csc2 x − 2
13.
15.
17.
cot x−tan x
x−cot x)
cot x+tan x
=cos2x 14. sin 2x =2(tan
tan 2 x−cot 2 x
2 cos 2x
sin 2x =cotx − tan x 16. tan 2x = 2
cot x−tan x
sin x
1+cos x +1+cos x
sin x
= 2 csc x 18. tan x +cotx = 2 csc(2x)
19. cos(2x) = cot2 x−1
cot 2 x+1
20. sin(2x) = 2tanx
1+tan 2 x
21.
23.
2sin 2 x
sin(2x) +cotx = sec x csc x 22. sec2 x cos(2x) =sec 2 x − 2tan 2 x
cos(2x)
sin x +sinx = csc x − sin x 24. 2tanx−sin(2x)
2sin 2 =tanx
x