Mathematics - Trigonometric Functions, Identities and Equation

Question - 1

In the acute angled triangle, the least value of secA + secB + secC is 

  • A 3
  • B 4
  • C 5
  • D 6

Question - 2

The value of tanA + 2 tan2A + 4 tan4A + 8 cot8A is

  • A cot A
  • B tan A
  • C cos A
  • D sin A

Question - 3

If \(tan\frac { \alpha }{ 2 } \quad and\quad tan\frac { \beta }{ 2 } \) are roots of the equations, then the value of cos \(\left( \alpha +\beta \right) \) is

  • A \(\frac { 627 }{ 725 } \)
  • B \(\frac { -627 }{ 725 } \)
  • C \(\frac { 726 }{ 725 } \)
  • D None of these

Question - 4

The value of \({ sin6 }^{ \circ }.{ sin }42^{ \circ }.{ sin66 }^{ \circ }.{ sin78 }^{ \circ }\)is

  • A \(\frac { 1 }{ 13 } \)
  • B \(\frac { 1 }{ 14 } \)
  • C \(\frac { 1 }{ 15 } \)
  • D \(\frac { 1 }{ 16 } \)

Question - 5

If \(msin\theta =nsin(\theta +2\alpha ),\) then \(tann(\theta +\alpha ).cot\alpha \) is equal to 

  • A \(\left( m+n \right) \left( m-n \right) \)
  • B \(\frac { m-n }{ m+n } \)
  • C \(\frac { m+n }{ m-n } \)
  • D \(2(m+n)(m-n)\)

Question - 6

\(cos2\theta cos2\phi +{ sin }^{ 2 }\left( \theta -\phi \right) \) is equal to 

  • A \(sin2\left( \theta +\phi \right) \)
  • B \(cos2\left( \theta +\phi \right) \)
  • C \(sin2\left( \theta -\phi \right) \)
  • D \(cos2\left( \theta -\phi \right) \)

Question - 7

The value of cos12o + cos84o + cos156o + cos132o is 

  • A 1/2
  • B 1
  • C -1/2
  • D 1/8

Question - 8

If \(cos\alpha +cos\beta =0\quad and\quad sin\alpha +sin\beta =0,\quad then\quad cos2\alpha +cos2\beta \) is equal to 

  • A \(2cos\left( \alpha +\beta \right) \)
  • B \(-2cos\left( \alpha +\beta \right) \)
  • C \(3cos\left( \alpha +\beta \right) \)
  • D \(None\quad of\quad the\quad above\)

Question - 9

If \(cos(\theta +\phi )=mcos(\theta -\phi ),\) then \(\frac { 1-m }{ 1+m } cot\phi \) is equal to 

  • A \(tan\theta \)
  • B \(-tan\theta \)
  • C \(2tan\theta \)
  • D \(None\quad of\quad these\)

Question - 10

If \(acos2\theta +bsin2\theta =c\quad has\quad \alpha \quad and\quad \beta \) as its roots, then \(tan\alpha +tan\beta \)  is equal to 

  • A \(-\frac { 2b }{ a+c } \)
  • B \(\frac { 2b }{ a+c } \)
  • C \(\frac { 3b }{ a+c } \)
  • D \(None\quad of\quad the\quad above\)
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