Mathematics - Trigonometry

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Question - 1

If sin A = sin B and cos A = cos B, then

  • A \(sin{1\over2}(A+B)=0\)
  • B \(sin{1\over2}(A-B)=0\)
  • C \(cos{1\over2}(A+B)=0\)
  • D \(cos{1\over2}(A-B)=0\)

Question - 2

If cos \(\theta\) + sin \(\theta\) = \(\sqrt2\) cos \(\theta\) then cos \(\theta\) - sin \(\theta\) =

  • A \(\sqrt2\) cos \(\theta\)
  • B \(\sqrt2\) sin \(\theta\)
  • C \(\sqrt2\) (cos \(\theta\) + sin \(\theta\))
  • D None of these

Question - 3

The equation sin2 \(\theta\) = \(x^{2}+y^{2}\over2xy\),is posible if

  • A x=y
  • B x=-y
  • C 2x=y
  • D None of these

Question - 4

If sin3 x sin 3x =\(\sum _{ m=0 }^{ n }{ = } { c }_{ m }\)  cos mx ,where c0,c1,c2,......cn \(\neq \) 0, is an identify in x then n =

  • A 5
  • B 6
  • C 7
  • D 8

Question - 5

The value of the expression \(1-\frac { { \sin { } }^{ 2 }y }{ 1+\cos { \quad y } } +\frac { 1+\cos { \quad y } }{ sin\quad y } -\frac { sin\quad y }{ 1-\cos { \quad y } } \),is

  • A 0
  • B 1
  • C sin y
  • D cos y

Question - 6

If sin A,cos A,tan A are in G.P..,then cot6A - cot2A  , equals

  • A 0
  • B -1
  • C 1
  • D None of these

Question - 7

If sin x + sin2x =1 ,then value of cos2x+cos4x is

  • A 1
  • B 2
  • C 1.5
  • D None of these

Question - 8

The period of the function 4cos3 \(\theta\)-3cos \(\theta\) is

  • A \(\pi\over3\)
  • B \(\pi\over4\)
  • C \(2\pi\over3\)
  • D None of these

Question - 9

If \(xcos\theta = y cos\left( \theta +\frac { 2\pi }{ 3 } \right) =zcos\left( \theta +\frac { 4\pi }{ 3 } \right) \) ,then value of xy+yz+zx is

  • A 0
  • B 1
  • C 2
  • D None of these

Question - 10

The value of tan 3x-tan 2x-tan x is 

  • A tan x tan 2x tan 3x
  • B - tan x tan 2x tan 3x
  • C tan x tan 2x - tan 2x tan 3x -tan 3x tan x
  • D None of these
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