Trigonometry Three Marks Questions

11th Standard

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Maths

Time : 00:45:00 Hrs
Total Marks : 30
    10 x 3 = 30
  1. Expand cos (A + B + C). Hence prove that cos A cos B cos C = sin A sin B cos C + sin B sin C cos A + sin C sin A cos B, if A + B + C = \(\frac{\pi}{2}\)

  2. What must be the radius of a circular running path, around which an athelete must run 5 times in order to describe 1 km?

  3. In a circular of diameter 40 cm, a chord is of length 20 cm. FInd the length of the minor is of the chord?

  4. if in two Circles, arcs of the same length subtend angles 600 and 750 at the center, find the ratio of their radii?

  5. Prove that sin 75o - sin 15o = cos 105o + cos 15o

  6. Prove that sin8x-cos8x=(sin2x-cos2x)(1-2sin2xcos2x)

  7. Prove that 4 cos 12° cos 48° cos 72° = cos 36°

  8. Prove that 1 + cos 2x + cos 4x + cos 6x = 4 cos x cos 2x cos 3x.

  9. If \(\sec x=\sqrt2\) and \(\frac{3\pi}{2}<x<2\pi.\) Find the value of \(\frac{1+\tan x+cosec x}{1+\cot x-cosec x}\)

  10. Prove that 2\(sin^{ 2 }\frac { 3\pi }{ 4 } +2cos^{ 2 }\frac { \pi }{ 4 } +2sec^{ 2 }\frac { \pi }{ 3 } \)=10

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