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 $None\quad of\quad the\quad above$