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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

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

square root of 2 plus 1

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

rightwards double arrow space space space sin space straight theta space plus space cos space straight theta space equals space square root of 2 space cosθ rightwards double arrow space space space space space sin space straight theta space equals space square root of 2 space cos space straight theta space minus space cos space straight theta rightwards double arrow space space space space sin space straight theta space equals space cos space straight theta space left parenthesis square root of 2 minus 1 right parenthesis

rightwards double arrow space space space fraction numerator cos space straight theta over denominator sin space straight theta end fraction space equals space fraction numerator 1 over denominator square root of 2 minus 1 end fraction rightwards double arrow space space space space cot space straight theta space equals space fraction numerator 1 over denominator square root of 2 minus 1 end fraction cross times fraction numerator left parenthesis square root of 2 plus 1 right parenthesis over denominator left parenthesis square root of 2 plus 1 right parenthesis end fraction space space space space equals space fraction numerator square root of 2 plus 1 over denominator 2 minus 1 end fraction space equals space 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

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

288 Views

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

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

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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

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

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Previous Year Papers

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Multiple Choice Questions

34. If then the value of is