Trigonometry Book Back Questions

11th Standard

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Maths

Time : 00:45:00 Hrs
Total Marks : 30
    5 x 1 = 5
  1. If cos280+sin280=k3, then cos 170 is equal to

    (a)

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

    (b)

    -\(\frac { { k }^{ 3 } }{ \sqrt { 2 } } \)

    (c)

    ±\(\frac { { k }^{ 3 } }{ \sqrt { 2 } } \)

    (d)

    -\(\frac { { k }^{ 3 } }{ \sqrt { 3 } } \)

  2. If \(\pi <2\theta <\frac { 3\pi }{ 2 } \), then \(\sqrt { 2+\sqrt { 2+2\quad cos4\theta } } \) equals to

    (a)

    -2 cosፀ

    (b)

    -2 sinፀ

    (c)

    2 cosፀ

    (d)

    2 sinፀ

  3. If cospፀ+cosqፀ=0 and if p≠q, then ፀ is equal to (n is any integer)

    (a)

    \(\frac { \pi (3n+1) }{ p-q } \)

    (b)

    \(\frac { \pi (2n+1) }{ p-q } \)

    (c)

    \(\frac { \pi (n\pm 1) }{ p\pm q } \)

    (d)

    \(\frac { \pi (n+2) }{ p+q } \)

  4. In a triangle ABC, sin2A+sin2B+sin2C=2, then the triangle is

    (a)

    equilateral triangle

    (b)

    isosceles triangle

    (c)

    right triangle

    (d)

    scalene triangle

  5. The triangle of maximum area with constant perimeter 12m

    (a)

    is an equilateral triangle with side 4m

    (b)

    is an isosceles triangle with sides 2m;5m;5m

    (c)

    is a triangle with sides 3m;4m;5m

    (d)

    Does not exist

  6. 3 x 2 = 6
  7. A fighter jet has to hit a small target by flying a horizontal distance. When the target is sighted, the pilot measures the angle of depression to be 300. If after 100km, the target has an angle of depression of 450, how far is the target from the fighter jet at that instant?

  8. Suppose that a satellite in space, an earth station and the centre of earth all in the same plane. Let r be the radius of earth and R be the distance from the centre of earth to the satellite. Let d be the distance from the earth station to the satellite. Let 30 be the angle of elevation from the earth station to the satellite. If the line segment connecting earth station and satellite substends angle at the centre of earth, then prove that d=\(\sqrt { 1+\left( \frac { r }{ R } \right) ^{ 2 }-2\frac { r }{ R } cos\alpha } \) .

  9. if x = \(\sum _{ n=0 }^{ \infty }{ { cos }^{ 2n } } \theta ;\) y = \(y=\sum _{ n=0 }^{ \infty }{ { sin }^{ 2n } } \theta \) and z = \(\sum _{ n=0 }^{ \infty }{ { cos }^{ 2n }\theta } \) sin2n\(\theta \), 0 < \(\theta \) < \(\frac { \pi }{ 2 } \),then show that xyz = x+y+z  
    Hint :1+x+x2+x3+.......= \(\frac { 1 }{ 1-x } \)where \(\left| x\right| \)< 1].

  10. 3 x 3 = 9
  11. 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 cos (A - B)

  12. If \(\cos { \left( \alpha -\beta \right) } +\cos { \left( \beta -\gamma \right) } +\cos { \left( \gamma -\alpha \right) } =\frac { -3 }{ 2 } \) then prove that \(\cos { \alpha } +\cos { \beta } +\cos { \gamma } =\sin { \alpha } +\sin { \beta } +\sin { \gamma } =0\)

  13. Prove that (1 + sec 2\(\theta\)) (1 + sec 4\(\theta\)) ... (1 + sec 2n\(\theta\)) = tan 2n\(\theta\) . cot \(\theta\).

  14. 2 x 5 = 10
  15. if \(\frac { cos^{ 4 }\alpha }{ { cos }^{ 2 }\beta } +\frac { { sin }^{ 4 }\alpha }{ { sin }^{ 2 }\beta } =1\) prove that \({ sin }^{ 4 }\alpha +{ sin }^{ 4 }\beta =2{ sin }^{ 2 }\alpha { sin }^{ 2 }\)

  16. Find a quadratic equation whose roots are sin 15and cos 15o

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