In a ∆ABC, if tanA2 = 56 and&

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 Multiple Choice QuestionsMultiple Choice Questions

131.

cos4π8 + cos43π8 +cos45π8 + cos47π8 is equal to

  • 32

  • - 23

  • - 1

  • 1


132.

Number of solutions of the equationan tanx + secx = 2cosx lying in the interval 0, 2π is

  • 0

  • 1

  • 2

  • 3


133.

In a triangle ABC, if tanA2 = 56 and tanB2 = 2037 , then a + c is equal to

  • b

  • 2b

  • 3b

  • 4b


134.

The angle of elevation of a jet fighter from a point A on the ground is 60°. After a flight of 10s, the angle of elevation changes to 30°. If thejet is flying at a speed of 432 km/h. Find the constant height at which thejet is flying.

  • 2003 m

  • 4003 m

  • 6003 m

  • 8003 m


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135.

In a ABC, if tanA2 = 56 and tanC2 = 25, then the sides a, b, c are in

  • AP

  • GP

  • HP

  • None of these


A.

AP

Given, tanA2 = 56 and tanC2 = 25 tanA2 + C2 = 56 + 251 - 56 × 25 = 3720 cotB2 = 3720  tanB2 = 3720 sinA = 2tanA21 + tan2A2 = 2 × 561 + 2536 = 6061sinB = 2tanB21 + tan2B2 = 2 × 20371 + 4001369 = 14801769sinC = 2tanC21 + tan2C2 = 2 × 251 + 425 = 2029Using sine rule,asinA = bsinB = csinC a6061 = b14801769 = c2029 = k a = 6061k, b = 14801769k, c = 2029kNow, a +c = 6061k + 2029k = 2960k1769    a + c = 2bHence, a, b and c are in AP.


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136.

The value of cosπ5cos2π5cos4π5cos8π5 will be

  • 116

  • - 116

  • 0

  • 12


137.

The function f(x) = sin(x) + cos(x) will be

  • an even function

  • an odd function

  • a constant function

  • None of these


138.

A balloon is coming down at the rate of4 m/min and its angle of elevation is 45° from a point on the ground which has been reduced to 30°, after 10 min. Balloonwill be on the ground at a distance ofhow many metres from the observer ?

  • 203 m

  • 203 + 3 m

  • 103 + 3 m

  • None of these


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139.

If sinθ + cscθ = 2, then sin2θ + csc2θ is equal to

  • 1

  • 4

  • 2

  • None of these


140.

The maximum value of 5cosθ + 3cosθ + π3 + 3 is

  • 10

  • - 10

  • 14

  • None of these


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