Trignometry - Important Question Paper

11th Standard

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Business Maths

Time : 01:00:00 Hrs
Total Marks : 50

    Part A

    10 x 1 = 10
  1. If \(\tan\theta=\frac{1}{\sqrt5}\) and \(\theta\) lies in the first quadrant, then \(\cos\theta\) is

    (a)

    \(\frac{1}{\sqrt6}\)

    (b)

    \(\frac{-1}{\sqrt6}\)

    (c)

    \(\frac{\sqrt5}{\sqrt6}\)

    (d)

    \(\frac{-\sqrt5}{\sqrt6}\)

  2. The value of 1-2sin245o is

    (a)

    1

    (b)

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

    (c)

    \(\frac14\)

    (d)

    0

  3. The value 4cos340o-3cos40o is

    (a)

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

    (b)

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

    (c)

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

    (d)

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

  4. The value of \(\frac{2\tan30^o}{1+tan^230}\) is

    (a)

    \(\frac12\)

    (b)

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

    (c)

    \(\frac{\sqrt{3}}{2}\)

    (d)

    \(\sqrt3\)

  5. If \(\sin A=\frac{1}{2}\) then \(4\cos^3A-3\cos A\) is

    (a)

    1

    (b)

    0

    (c)

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

    (d)

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

  6. 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)

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

  7. \(\sin\left(\cos^{-1}\frac{3}{5}\right)\) is

    (a)

    \(\frac{3}{5}\)

    (b)

    \(\frac{5}{3}\)

    (c)

    \(\frac{4}{5}\)

    (d)

    \(\frac{5}{4}\)

  8. The value of \(\frac{1}{cosec(-45^o)}\) is

    (a)

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

    (b)

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

    (c)

    \(\sqrt2\)

    (d)

    \(-\sqrt2\)

  9. If p sec 50o=tan 50o then p is

    (a)

    cos 50o

    (b)

    sin 50o

    (c)

    tan 50o

    (d)

    sec 50o

  10. \(\left(\frac{\cos x}{cosec x}\right)-\sqrt{1-\sin^2x}\sqrt{1-\cos^2x}\) is

    (a)

    cos2x-sin2x

    (b)

    sin2x-cos2x

    (c)

    1

    (d)

    0

  11. Part B

    6 x 2 = 12
  12. Solve: \(\tan^{-1}2x+\tan^{-1}3x=\frac{\pi}{4}\)

  13. Determine the quadrants in which the following degree lie. 1195°

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

  15. Find the values of the following trigonometric ratios. \(\sec { \left( { 390 }^{ o } \right) } \)

  16. Find the values of the following trigonometric ratios. \(\tan { \left( { -855 }^{ o } \right) } \)

  17. Find the values of each of the following trigonometric ratios.  \(cosec { \left( { 1125 }^{ o } \right) } \)

  18. Part C

    6 x 3 = 18
  19. If \(\sin A=\frac35\) where \(0<A<\frac { \pi }{ 2 } \) and \(cosB=\frac { -12 }{ 13 } ,\pi <A<\frac { 3\pi }{ 2 } \) find the value of 
    \(\tan(A-B)\)

  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. If \(\cos { A } =\frac { 13 }{ 14 } \quad \)and \(\cos { B } =\frac { 1 }{ 7 } \) where A, B are acute angles, prove that A-B=\(\frac { \pi }{ 3 } \)

  22. Prove that 2 tan 80° = tan 85° - tan 5°.

  23. If A+B=45° , Prove that (1 + tan A) (1+ tan B) = 2 and hence deduce the value of \(\tan { 22{ \frac { 1 }{ 2 } }^{ ° } } \)

  24. Find all other trigonometrical ratios if \(\sin x=\frac{-2\sqrt6}{5}\) and x lies in III quadrant?

  25. Part D

    2 x 5 = 10
  26. Prove that sin(n+1)x sin(n+2) x+cos(n+1)xcos(n+2)x=cosx.

  27. Prove that cos22x-cos26x = sin 4x.sin 8x

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