Trigonometry Two Marks Questions

10th Standard EM

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Maths

Time : 00:45:00 Hrs
Total Marks : 20
    10 x 2 = 20
  1. prove that\(\left( \frac { co{ s }^{ 3 }A-si{ n }^{ 3 }A }{ cosA-sinA } \right) -\left( \frac { co{ s }^{ 3 }A+si{ n }^{ 3 }A }{ cosA+sinA } \right) =2sinAcosA\)

  2. prove that \(\frac { sinA }{ secA+tanA-1 } +\frac { cosA }{ cosecA+cotA-1 } =1\)

  3. As observed from the top of a 60 m high light house from the sea level, the angles of depression of two ships are 28° and45°. If one ship is exactly behind the other on the same side of the lighthouse, find the distance between the two ships.
    (tan28°=0.5317)

  4. A man is watching a boat speeding away from the top of a tower. The boat makes an angle of depression of 60° with the man’s eye when at a distance of 200 m from the tower. After 10 seconds, the angle of depression becomes 45°. What is the approximate speed of the boat (in km / hr), assuming that it is sailing in still water?(\(\sqrt { 3 } \)=1.732)

  5. If tan A=\(\frac{3}{4}\), then sin A cos A=\(\frac{12}{15}\)

  6. (sin ∝+cos ∝)(tan ∝+cot ∝)=sec ∝+cosec ∝

  7. \(\sqrt3\)1 (3-cot30o)=tan3 60o-2sin60o

  8. A ladder 15 metres long just reaches the top of a vertical wall. If the ladder makes an angle of 60o with the wall, finf the height of the wall.

  9. Simplify (1+tan2θ)(1-sinθ)(1+sinθ)

  10. If 2sin2θ-cos2θ=2, then find the value θ.

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