. 2tan 2l tan 2T
6 sinxcos x2 sin" x cos 3x cos x 2 sin x cos x cos
3.2. sinxcos 2x+cosx cos4x= sin( ~+ 2x)
3.3. sin 2x~cos! ~ - sins ~
3.4. (1+cos4x)sin 2x= cos-2x.
3.5. sin"2z +sin" 3z +sin''4z +sin25z = 2.
3.6. sin 2xsin 6x - cos2x cos Gx = V2sin 3xcos 8x.
3.7. sin 3x cos 3x = sin 2.T.
3.8. cos2x - 5 sin x - 3 = O. 3.9. 3 sin 2x + 2 cos 2x = 3.
3.10. cot (3; _x) +cot"X+ 1~~~Sx2x = O. 3.11. 6 sin" x +sin x cos x - cos"X = 2. 3.12. cos7x + sin 8x = cos 3x - sin 2x.
3.13. sin" x - 2 sin x cos x = 3 cos"x:
3.14. cos 5x + cos7x = cos (:rt + 6x).
3.15. 4sinxcos (~ -x)+4sin(:rt+x)cosx
+2sin (32J't - x) cos (:rt+x) = 1. 3.16. sin x - sin 2x +sin 5x +sin 8x = O.
3.17. 2 sin z - cos z = 2/5.
3.18. cos ( ; +5x)+sin x=2 cos3,T.
3.19. (1+sinx)tan ( ~ - ; )= co~x -cosa;
3.20. cos x - V3'sin x = cos 3x.
3.21. sin 2z + 5 (sin z + cos z) + 1 = O. 3.22. sin"2t+cos"2t+ ; sin4t= 1. 3.23. tan z tan 2z = tan z + tan 2z.
3 2'" sin3x+cos3x 2
" 'to 2cos x--sinx = cos x.
3 '25 cot4t +~=O
• • sin 2 t sin2 4t .
3.26. tan4x = 36 cos"2x.
3.27. cot x - tan x - 2 tan 2x - 4 tan 4x + 8 = O. 3.28. 4 sin" x cos3x + 4 cos"x sin 3x = 3 sin 2x.
3.29. 2 coszsin" ( 3; -z) - 5 sin2zcos2Z
Problems
3.30. sin 2x sin 6x cos 4x + ~ cos 12x=0.
3.31. COS5~x + sin4ux = 1. 3.32. logcosx sin x = 1.
3.33. cot (sin x) = 1.
3.34. tan 5.1: - 2tan 3x = tan 5x tan" 3x.
, cos2x
3.35. cotx - 1= tanx+1
36.3 . cos23+ 1x 4cOS x -2 - cos 3x cos x.4
3.37. Find all the solutions of the equation
1 + cos x + cos 2x + sin x + sin 2x + sin 3x,
which satisfy the condition ~ < 13x - ~ l~n.
3.38. Find all the solutions of the equation
2 - V3cos 2x + sin 2:1: = 4 cos23x,
which satisfy the inequality cos (2x- : ) >0.
3.39. Solve the equation
111
~ f 1- 4cos24x2 . = cos (2x _ ~ ) .
V 8cos (2x - -f) )
3.40. Find all the solutions of the equation
2+cos; x+V3sin ~ x=4sin2 ~ , satisfying the condition sin ( ; +~ )> 0.
3.41. Show that the equation
1
cot 2x + cot 3x + .Sillxsm. 2xsm. 3x =°
has no roots.
3.42. Find all the solutions of the equation
4 (3V4x-x2sin2( xty )+2eos(x+y»)
= 13+4cos2(x+y)
x+yc-c n/4.
tan x tan y'-=1/6.
V-Zsin x=siny,