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The value of following is
$3 left parenthesis sin to the power of 4 straight theta space plus space cos to the power of 4 straight theta right parenthesis space plus space 2 left parenthesis sin to the power of 6 straight theta space plus space cos to the power of 6 straight theta right parenthesis space plus space 12 space sin squared space cos squared straight theta$

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12.

If $secθ plus space tanθ space equals space 2 plus square root of 5 comma$ then the value of $sinθ$ is $left parenthesis 0 degree less-than or slanted equal to straight theta less-than or slanted equal to 90 degree right parenthesis$

$fraction numerator square root of 3 over denominator 2 end fraction$
$fraction numerator 1 over denominator square root of 5 end fraction$
$fraction numerator 2 over denominator square root of 5 end fraction$
$fraction numerator 2 over denominator square root of 5 end fraction$

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13.
The value of $left parenthesis secθ space plus space cosecθ right parenthesis space$ when $straight theta space equals space 45 degree$ is

$3 square root of 2$
$4 square root of 2$
$2 square root of 2$
$2 square root of 2$

2 square root of 2

Here $straight theta space equals 45 degree$
$therefore space space secθ plus space cosecθ space equals space sec space 45 degree space plus space cosec space 45 degree$
$equals space square root of 2 plus square root of 2 space equals space 2 square root of 2$

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14.

fraction numerator tan squared straight theta over denominator secθ plus 1 end fraction minus secθ

is equal to

-1
1
0
0

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15.

sin to the power of 6 straight theta plus cos to the power of 6 straight theta

is equal to

$1 minus 3 sin squared θcos squared straight theta$
$1 minus 3 sinθ space cosθ$
$1 plus 3 sin squared θcos squared straight theta$
$1 plus 3 sin squared θcos squared straight theta$

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16.

If $tanθ plus cotθ space equals space 2 comma space space space 0 less than straight theta less than 90 degree comma$ then the value of $straight theta$ is

$30 degree$
$45 degree$
$60 degree$
$60 degree$

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17.

The expression of $1 plus fraction numerator cot squared straight A over denominator 1 plus cosecA end fraction$ is equal to

sin A
cos A
tan A
tan A

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18.

Given that $tan left parenthesis straight theta plus 15 degree right parenthesis space space equals space square root of 3$ . Then the value of $straight theta$ is:

$15 degree$
$75 degree$
$45 degree$
$45 degree$

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19.

If $sec squared straight theta space plus space tan squared straight theta space equals space square root of 3$ , then the value of $sec to the power of 4 straight theta space minus space tan to the power of 4 straight theta$ is

$fraction numerator 1 over denominator square root of 3 end fraction$
1
$square root of 3$
$square root of 3$

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20.

If $straight pi space sin space straight theta space equals space 1 comma space space straight pi space cosθ space equals space 1 comma space$ then the value of $open curly brackets square root of 3 tan open parentheses 2 over 3 straight theta close parentheses plus 1 close curly brackets$ is