Trigonometry Model Question Paper

11th Standard

    Reg.No. :
  •  
  •  
  •  
  •  
  •  
  •  

Maths

Time : 01:00:00 Hrs
Total Marks : 50
    5 x 1 = 5
  1. \(\frac { 1 }{ cos{ 80 }^{ 0 } } -\frac { \sqrt { 3 } }{ sin{ 80 }^{ 0 } } \)=

    (a)

    \(\sqrt{2}\)

    (b)

    \(\sqrt{3}\)

    (c)

    2

    (d)

    4

  2. cos10+cos20+cos30+: : :+cos1790=

    (a)

    0

    (b)

    1

    (c)

    -1

    (d)

    89

  3. \(\frac { sin(A-B) }{ cosAcosB } +\frac { sin(B-C) }{ cosBcosC } +\frac { sin(C-A) }{ cosCcosA } \) is

    (a)

    sinA+sinB+sinC

    (b)

    1

    (c)

    0

    (d)

    cosA+cosB+cosC

  4. If tanA=\(\frac { a }{ a+1 } \) and B=\(\frac { 1 }{ 2a+1 } \) then the value of A+B is

    (a)

    0

    (b)

    \(\frac { \pi }{ 2 } \)

    (c)

    \(\frac { \pi }{ 3 } \)

    (d)

    \(\frac { \pi }{ 4 } \)

  5. cosp=\(\frac { 1 }{ 7 } \) and cosQ=\(\frac { 13 }{ 14 } \) where P,Q are angles, then P-Q is

    (a)

    \(\frac { \pi }{ 6 } \)

    (b)

    \(\frac { \pi }{ 3 } \)

    (c)

    \(\frac { \pi }{ 4 } \)

    (d)

    \(\frac { 5\pi }{ 12 } \)

  6. 5 x 2 = 10
  7. Find the value of tan \(\frac{7\pi}{12}\).

  8. Prove that \(\sin { \left( \pi +\theta \right) } =-\sin { \theta } \)

  9. If cosA=\(\frac { 4 }{ 5 } \), cosB=\(\frac { 12 }{ 13 } ,\frac { 3\pi }{ 2 } \)\(\pi \), find cos(A+B)

  10. Prove that \(\frac { cos9x-cos5x }{ sin17x-sin3x } =-\frac { sin2x }{ cos10x } \)

  11. In a ΔABC if a=3, b=5 and c=7, find cosA and cosB.

  12. 5 x 3 = 15
  13. If sin A = \(\frac{3}{5}\) and cos B = \(\frac{9}{41}\), 0 < A < \(\frac{\pi}{2}\), 0 < B < \(\frac{\pi}{2}\). Find the value of sin (A + B)

  14. Find cos(x - y), given that cos x = \(-\frac{4}{5}\) with \(\pi<x<{{3\pi}\over{2}}\) and sin y = \(-\frac{24}{25}\) with\(\pi<y<{{3\pi}\over{2}}\).

  15. if a cos \(\theta\) -b sin \(\theta\) = C Show that a sin \(\theta\) +b cos \(\theta\) = \(\pm \sqrt { { a }^{ 2 }+{ b }^{ 2 }-{ c }^{ 2 } } \)

  16. Prove that cos \(\left( {{3\pi}\over{4}}+\pi\right)-cos\left({{3\pi}\over{4}}-4\right)=-\sqrt{2}sin\ x.\)

  17. If \(2cos\theta=x+\frac{1}{x}\) then prove that \(2\theta=\frac{1}{2}(x^2+\frac{1}{x^2})\)

  18. 4 x 5 = 20
  19. if sin \(\theta\) + cos \(\theta\) = m, show that cos6\(\theta\) + sin6\(\theta\)  = \(\frac { 4-3({ m }^{ 2 }-1)^{ 2 } }{ 4 } \) where m2 \(\le \) 2

  20. Prove that \(sin\frac { \theta }{ 2 } sin\frac { 7\theta }{ 2 } +sin\frac { 3\theta }{ 2 } sin\frac { 11\theta }{ 2 } =sin2\theta sin5\theta \)

  21. If the sides of a \(\triangle\)ABC are a = 4, b = 6, and c = 8, show that \(4\cos { B } +3\cos { C } =2\)

  22. Show that \(\sin ^{ -1 }{ \left( \frac { 12 }{ 13 } \right) } +\cos ^{ -1 }{ \left( \frac { 4 }{ 5 } \right) } +\tan ^{ -1 }{ \left( \frac { 63 }{ 16 } \right) } =\pi \)

*****************************************

TN 11th Standard Maths free Online practice tests

Reviews & Comments about 11th Maths - Trigonometry Model Question Paper

Write your Comment