#### 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.