Important 5 mark questions paper

11th Standard

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Maths

Use blue pen Only

Time : 00:50:00 Hrs
Total Marks : 75

    Part A

    Answer all the questions

    15 x 5 = 75
  1. Find all the angle between 0o and 360o which satisfy the equation \(\sin ^{ 2 }{ \theta } =\frac { 3 }{ 4 } \)

  2. Show that \(\sin ^{ 2 }{ \frac { \pi }{ 18 } } +\sin ^{ 2 }{ \frac { \pi }{ 9 } } +\sin ^{ 2 }{ \frac { 7\pi }{ 18 } } +\sin ^{ 2 }{ \frac { 4\pi }{ 9 } } =2\)

  3. Show that\(\frac { sin8x\quad cosx-sin6x\quad cos3x }{ cos2x\quad cosx-sin3x\quad sin4x } =tan2x\)

  4. Show that \(\frac { (cos\theta -cos3\theta )(sin8\theta +sin2\theta ) }{ (sin5\theta -sin\theta )(cos4\theta -cos6\theta ) } =1\)

  5. Prove that\(\frac { sin4x+sin2x }{ cos4x+cos2x } =tan3x\)

  6. Prove that \(\frac { cot(180+\theta )sin(90-\theta )cos(-\theta ) }{ sin(270+\theta )tan(-\theta )cosec(360+\theta ) } ={ cos }^{ 2 }\theta cot\theta \)

  7. Find the values of other five trigonometric functions for the following
    Cos \(\theta\) = -\(\frac { 1 }{ 2 } \) \(\theta\) lies in the III quadrant

  8. In \(\triangle\)ABC, 60° prove that b + c = 2a cos \(\left( \frac { B-C }{ 2 } \right) \)

  9. In \(\triangle\)ABC, Prove the following a sin \(\left( \frac { A }{ 2 } +B \right) \)=(b+c) sin \(\frac { A }{ 2 } \)

  10. In \(\triangle\)ABC, Prove the following
    \(\frac { asin(B-C) }{ { b }^{ 2 }-{ c }^{ 2 } } =\frac { bsin(C-A) }{ { c }^{ 2 }-{ a }^{ 2 } } =\frac { csin(A-B) }{ { a }^{ 2 }-{ b }^{ 2 } } \)

  11. In a \(\triangle \)ABC, if \(\frac { sin\quad A }{ sin\quad C } =\frac { sin(A-B) }{ sin(B-c) } \),prove that a2,b2,c2are in arithmetic progression 

  12. If A + B + C = \(\pi\), prove the following
    cos A + cos B + cos C = 1 + 4 sin \(({A\over 2})\)sin \(({B\over 2})\)sin\(({C\over 2})\)

  13. Solve\(\sqrt{3}\)  sin \(\theta\) - cos \(\theta\) =\(\sqrt{2}\)

  14. In a triangle  ABC, prove that \({a^2+b^2\over a^2+c^2}={1+cos(A-B)cos C\over 1+cos (A-C)cos B}\)

  15. Suppose two radar stations located 100 km apart, each detect a fighter aircraft between them. The angle of elevation measured by the first station is 30°, whereas the angle of elevation measured by the second station is 45°. Find the altitude of the aircraft at that instant.

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