TOPIC GENERAL SOLUTIONS OF TRIGONOMETRIC EQUATIONS VIRUPAXI. B.DODAMANI

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1 TOPIC GENERAL SOLUTIONS OF TRIGONOMETRIC EQUATIONS VIRUPAXI. B.DODAMANI Lecturer in Mathematics Govt Chintamanrao P.U College Belgaum Ph:

2 1) One of the solution of the equation 2cosθ+1=0 is a) θ=2π/3 c) θ=-π/3 b) θ=π/3 d) θ=π 2) The general solution of the equation tan(θ/2)=-1 is a) θ=2nπ±π/2 c) θ=2nπ+π/2 b) θ=nπ-π/2 d) θ=2nπ-π/2 3) The general solution of the equation 2cos3x+1=0 is a) x=2nπ ± π c) x=2nπ ± π b) x=nπ + π d) x=2nπ ± π ) If cos(α+β)=4/5 and sin(α-β)=5/13 then tan2α is a) 21/65 c) 56/33 b) 99/29 d) 29/99 5) The general solution of cosx+sinx- 2=0 is a) x=nπ + π c) x=2nπ + π 4 4 b) x=nπ - π d) x=2nπ - π 4 4 6) If tan 2 θ - ( 3+1/ 3)tanθ+1=0 then θ is a) 2nπ + π c) nπ + π/4 b) nπ + π/2 d) nπ + π/3 or nπ + π/6 7) The equation e sinx e -sinx -4 = 0 has a) Only one solution c) Infinite number of solutions b) No real solution d)one real and one imaginary solution

3 8) The solution of the equation (sinx+cosx) 1+sin2x = 2, -π x π is a) π/2 c) π/4 b) π/3 d) π 9) The general solution of cos 100 x sin 100 x =1 is a) x=2nπ c) x=nπ b) x=2nπ±π/3 d) x=nπ+(-1) n π/2 10) If log 2 sinx log 2 cosx log 2 (1-tan 2 x) = 1, The general solution a) x=nπ +π/4 c) x=1/8(4n+1)π b) x=1/2(4n+1)π d) x=1/4(4n+1)π 11) If (1- tanθ)(1+tanθ)+2tan 2 θ = 0 then θ in (-π/2, π/2) is Cos 2 θ a) ±π/3 c) ±π/6 b) π/4 d) π/4 12) The values of θ satisfying both the equations sinθ= -1/2 and tanθ=1/ 3 are a) 30, 210 c) 210, 570 b) 30, 390 d) -30, ) The general solution of sinx/3=3/2 is a) 3nπ+(-1) n π/3 c) nπ+(-1) n π/3 b) 3nπ+(-1) n π d) none of these 14) The general solution of cot2x - tan2x = 2 is a) x=nπ + π c) x=nπ + π b) x=nπ + π d) none of these 2 16

4 15) The sec2θ, 2 and sin2θ are in H.P then θ= a) nπ ; nπ+π/2 c) nπ; nπ+π/4 b) nπ+π/4 d) nπ 16) The general solution of the equation tan3x+tanx=0 is a) nπ/2 c) nπ/4 b) nπ+π/4 d) none of these 17) The general solution of cos 2 θ=cos 2 α is a) θ=2nπ±α c) θ=nπ±(-1) n α b) θ=nπ ±α d) none of these 18) If then x=? a) 2nπ ± π/2 c) nπ ± π/2 b) nπ+(-1) n π/2 d) none of these 19) If tan 2 x+cot 2 x=2 then x=? a) nπ±π/4 c) 2nπ±π/4 b) nπ-π/4 d) nπ+π/4 20) If cos 2 x+1+sinx=0 then x=? a) 2nπ±π/2 c) nπ+(-1) n π/2 b) 2nπ±π d) nπ+(-1) n (-π/2) 21) Find the general solution of a) x=2nπ±π/3 ; 2nπ±2π/3 c) x=nπ±π/6; 2nπ±3π/4 b) x=2nπ±π/3; 2nπ±3π/4 d) none of these 22) If 1+cosx+cos 2 x+ upto infinity=4+2 3 then x=? a) 2nπ±π/3 c) 2nπ±π/6 b) 2nπ±π/4 d) none of these

5 23) The general solution of sinx =cosx is given by x=? (a) nπ+π/4 c) 2nπ±π/4 (b) nπ±π/4 d) nπ-π/4 24) If cosθ,sinθ, tanθ are in G.P then θ = a) 2nπ c) (2n+1)π/2 b) nπ/2 d) nπ 25) The number of solution between 0 and 2π of cos3θ = sin2θ is a) 2 c) 4 b) 8 d)6 26) If (1+tanθ)(1+tanΦ) = 2 then θ+φ=? a) 30 c) 75 b) 60 d) 45 27) The equation 2cos 2 (x/2)sin 2 x = x 2 +1/x 2 0 x π/2 has a) One real solution c) no solution b) More than one solution d) none of these 28) The values of θ satisfying sin7θ=sin4θ-sinθ and 0 < θ< π/2 are a) π/3, π/4 c) π/9, π/4 b) π/3, π/9 d) π/6, π/9 29) If 5cos2θ+2cos 2 (θ/2)+1=0, -π< θ<π then θ=? a) Cos -1 (3/5) c) π/3, Cos -1 (3/5) b) π/3 d) ± π/3 π- Cos -1 (3/5) 30) If tanθ+tan4θ+tan7θ = tanθtan4θtan7θ then =? a) nπ/12 c) nπ/7 b) nπ d) nπ/4

6 31) If cot 2 x (1+ 3)cotx + 3 =0 then the solution set in (0,π/2) is? a) π/3, π/6 c) π/6, π/4 b) π/3, π/4 d) None 32) If tanθtan(120-θ)tan(120+θ) =1/ 3 then θ=? a) x=nπ - π c) x=nπ - π b) x=nπ + π d) x=nπ + π nєi ) If 3tan(θ-15)=tan(θ+15), 0< θ <π then θ=? a) π/4 c) π/6 b) π/3 d) π/2 34) General solution of sin2θ=( 5-1)/4 then θ is? a) nπ+(-1) n π c) nπ+(-1) n π b) nπ+(-1) n 3π d) nπ+(-1) n π nєz ) If sinθsin(60+θ)sin(60-θ) =1/4 then θ=? a) nπ or (3n±1) π/9 c) 2nπ/3±π/9 b) nπ/3+π/18 d) nπ/3+(-1) n π/6 36) The general solution of the equation 1-sinx+ +(-1) n sin n x+. = 1-cos2x is? 1+sinx+ +sin n x+. 1-cos2x a) nπ+(-1) n π c) nπ+(-1) n π 3 6 b) nπ+(-1) n+1 π d) nπ+(-1) n-1 π 6 3

7 37) The general solution of 9 sinx -2 3 sinx +1 = 0 is a) nπ c) nπ+(-1) n π 2 2 b) nπ d) nπ 4 38) The general solution of 2cos 2 θ =1+cos(π/8) is a) 2nπ ± π c) nπ ± π 8 8 b) 2nπ ± π d) nπ ± π ) The general solution of x satisfying the equation 3sinx+cosx= 3 is given by a) x = nπ ± π c) x = nπ ± π 3 6 b) x =nπ +(-1) n π - π d) x = nπ +(-1) n π + π ) If x= sinθ and x+1/x = 5/2 then θ= a) nπ+(-1) n π c) nπ - (-1) n π 2 6 b) nπ+(-1) n π d) nπ +(-1) n π 6 3

8 ANSWERS 1. a 2. d 3. d 4. c 5. c 6. d 7. b 8. c 9. c 10. c 11. a 12. c 13. b 14. a 15. b 16. c 17. b 18. c 19. a 20. d 21. a 22. c 23. c 24. d 25. d 26. d 27. c 28. c 29. d 30. a 31. c 32. d 33. a 34. c 35. d 36. c 37. b 38. d 39. b 40. b

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