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Trigonometry

Multiple Choice Questions

31.

If tan⁴θ + tan²θ = 1 then the value of cos⁴θ + cos²θ is

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32.

The value of 8(sin⁶θ + cos⁶θ) - 12(sin⁴θ + cos⁴θ) is equal to

20
-20
-4
-4

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33.

(1 + sec 20° + cot 70°)(1 - cosec 20° + tan70°) is equal to

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34.

If $sin space straight theta space plus space cos space straight theta space equals space square root of 2 space sin space left parenthesis 90 degree space minus space straight theta right parenthesis comma$ then the value of $cot space straight theta$ is

$negative square root of 2 minus 1$
$square root of 2 minus 1$
$square root of 2 plus 1$
$square root of 2 plus 1$

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35.

If θ is a positive acute angle and 3(sec²θ + tan²θ) = 5, then the value of cos 2θ is

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

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36.
If $straight x space cos squared 30 degree. space sin space 60 degree space equals space space fraction numerator tan squared begin display style 45 end style degree. space sec space 60 degree over denominator cosec space 60 degree end fraction$ , then the value of x is

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

$2 2 over 3$
$2 2 over 3$

2 2 over 3

straight x. space cos squared 30 degree. space sin space 60 degree space equals space fraction numerator tan squared 45 degree. space sec space 60 degree over denominator cosec space 60 degree end fraction

rightwards double arrow space straight x space. space open parentheses fraction numerator square root of 3 over denominator 2 end fraction close parentheses squared. space fraction numerator square root of 3 over denominator 2 end fraction space equals space fraction numerator 1 cross times 2 over denominator begin display style fraction numerator 2 over denominator square root of 3 end fraction end style end fraction rightwards double arrow space space straight x space cross times space space 3 over 4 space cross times space fraction numerator square root of 3 over denominator 2 end fraction space equals space square root of 3 rightwards double arrow space space space straight x space equals space fraction numerator square root of 3 space cross times space 8 over denominator 3 square root of 3 end fraction space equals space 8 over 3 space equals space 2 2 over 3

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37.

If $tan space straight alpha space equals space 2 comma$ then the value of $fraction numerator cosec squared straight alpha space minus space sec squared straight alpha over denominator cosec squared straight alpha space plus space sec squared straight alpha end fraction$ is

$negative 15 over 9$
$negative 3 over 5$
$3 over 5$
$3 over 5$

170 Views

38.

If $sin left parenthesis straight theta space plus space 30 degree right parenthesis space equals space fraction numerator 3 over denominator square root of 12 end fraction comma$ then the value of $cos squared straight theta$ is

$1 fourth$
$fraction numerator square root of 3 over denominator 2 end fraction$
$3 over 4$
$3 over 4$

181 Views

39.

If $0 less or equal than straight theta less than 90 degree$ and $4 cos squared straight theta space minus space 4 square root of 3 cosθ space plus space 3 space equals space 0$ then the value of θ is

30°
45°
90°
90°

158 Views

40.

If $straight a space sin space straight theta space plus space straight b space cosθ space equals space straight c comma$ then $straight a space cos space straight theta space minus space straight b space sin space straight theta$ is equal to

$plus-or-minus square root of straight a plus straight b minus straight c end root$
$plus-or-minus square root of straight a squared plus straight b squared plus straight c squared end root$
$plus-or-minus square root of straight a squared plus straight b squared minus straight c squared end root$
$plus-or-minus square root of straight a squared plus straight b squared minus straight c squared end root$

280 Views

Previous Year Papers

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Multiple Choice Questions

36. If , then the value of x is