Trigonometry Model Question Paper

11th Standard

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Business Maths

Time : 01:00:00 Hrs
Total Marks : 50
    5 x 1 = 5
  1. The radian measure of 37o30' is

    (a)

    \(\frac{5\pi}{24}\)

    (b)

    \(\frac{3\pi}{24}\)

    (c)

    \(\frac{7\pi}{24}\)

    (d)

    \(\frac{9\pi}{24}\)

  2. The value of \(\sin(-420^o)\) is

    (a)

    \(\frac{\sqrt3}{2}\)

    (b)

    \(-\frac{\sqrt3}{2}\)

    (c)

    \(\frac{1}{2}\)

    (d)

    \(\frac{-1}{2}\)

  3. The value of cos245o-sin245o is

    (a)

    \(\frac{\sqrt3}{2}\)

    (b)

    \(\frac{1}{2}\)

    (c)

    0

    (d)

    \(\frac{1}{\sqrt{2}}\)

  4. The value of \(\frac{3\tan10^o-\tan^310}{1-3\tan^210}\) is

    (a)

    \(\frac{1}{\sqrt3}\)

    (b)

    \(\frac{1}{2}\)

    (c)

    \(\frac{\sqrt3}2\)

    (d)

    \(\frac{1}{\sqrt2}\)

  5. If \(\alpha\) and \(\beta\) be between 0 and \(\frac{\pi}{2}\) and if \(\cos(\alpha+\beta)=\frac{12}{13}\) and \(\sin(\alpha-\beta)=\frac{3}{5}\) then \(\sin2\alpha\) is 

    (a)

    \(\frac{16}{15}\)

    (b)

    0

    (c)

    \(\frac{56}{65}\)

    (d)

    \(\frac{64}{65}\)

  6. 5 x 2 = 10
  7. Prove that \(\tan^{-1}\left(\frac{4}{3}\right)-\tan^{-1}\left(\frac{1}{7}\right)=\frac{\pi}{4}\)

  8. Convert the following degree measure into radian measure 150o

  9. Find the values of the following trigonometric ratios. \(\sin { { 300 }^{ o } } \)

  10. Prove that \(sin^2\left(\frac{\pi}{8}+\frac x2\right)-sin^2\left(\frac{\pi}{8}-\frac x2\right)=\frac{1}{\sqrt2}\sin x.\)

  11. Evaluate\(\cos\left[\frac{\pi}{3}-\cos^{-1}\left(\frac{1}{2}\right)\right]\)

  12. 5 x 3 = 15
  13. Prove that  \(2\sin ^{ 2 }{ \frac { \pi }{ 6 } } +\ cosec ^{ 2 }{ \frac { 7\pi }{ 6 } } \cos ^{ 2 }{ \frac { \pi }{ 3 } } =\frac { 3 }{ 2 } \)

  14. Prove that: \(\cos { { 510 }^{ o } } \cos { { 330 }^{ o } } +\sin { { 390 }^{ o } } \cos { { 120 }^{ o } } =-1\)

  15. Show that \(\tan\left(\frac{\pi}{3}+x\right)\tan\left(\frac{\pi}{3}-x\right)=\frac{2\cos2x+1}{2\cos2x-1}\)

  16. Prove that \(\frac{\sin5x+\sin3x}{\cos5x+\cos3x}=\tan4x\)

  17. If tan(x + y) = 42 and x = tan–1(2), then find y

  18. 4 x 5 = 20
  19. If \(\cos(\alpha+\beta)=\frac45\) and \(\sin(\alpha-\beta)=\frac{5}{13}\) where \((\alpha+\beta)\) and \((\alpha-\beta)\) are acute, then find \(\tan2\alpha\)

  20. If \(\sin { A } =\frac { 3 }{ 5 } \) where\(0<A<\frac { \pi }{ 2 } \)  and  \(\cos { B } =\frac { -12 }{ 13 } \) ,   \(\pi <A<\frac { 3\pi }{ 2 } \) , find the values of the following sin (A - B)

  21. Prove that cot x cot 2x - cot 2x cot 3x - cot 3x cot x = 1.

  22. Prove that cos 4x = 1 - 8 sin2x cos2x.

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