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Trigonometry

Multiple Choice Questions

31.

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

1320 Views

32.

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

20
-20
-4
-4

1249 Views

33.
(1 + sec 20° + cot 70°)(1 - cosec 20° + tan70°) is equal to

0

1

2

2

left parenthesis 1 plus sec space 20 degree space plus space cot space 70 degree right parenthesis thin space left parenthesis 1 minus cosec space 20 degree space plus space tan space 70 degree right parenthesis space equals space left parenthesis 1 plus sec space 20 degree space plus space tan space 20 degree right parenthesis thin space left parenthesis 1 minus cosec space 20 degree space plus space cot space 20 degree right parenthesis open square brackets because space space tan space left parenthesis 90 degree space minus space straight theta right parenthesis space equals space cot space straight theta semicolon space space cot left parenthesis 90 degree space minus space straight theta right parenthesis space equals space tan space straight theta close square brackets

equals space open parentheses 1 plus fraction numerator 1 over denominator cos space 20 degree end fraction space plus space fraction numerator sin space 20 degree over denominator cos space 20 degree end fraction close parentheses space open parentheses 1 minus fraction numerator 1 over denominator sin space 20 degree end fraction plus fraction numerator cos space 20 degree over denominator sin space 20 degree end fraction close parentheses equals space open parentheses fraction numerator cos space 20 degree plus 1 space plus space sin space 20 degree over denominator cos space 20 degree end fraction close parentheses cross times open parentheses fraction numerator sin space 20 degree space minus space 1 space plus cos space 20 degree over denominator sin space 20 degree end fraction close parentheses equals space fraction numerator left parenthesis cos space 20 degree space plus space sin space 20 degree right parenthesis squared minus 1 over denominator sin space 20 degree. space cos 20 degree end fraction equals space fraction numerator cos squared 20 degree space plus space sin squared 20 degree plus 2. space sin 20 degree. space cos 20 degree minus 1 over denominator sin space 20 degree. space cos space 20 degree end fraction equals space 2

1467 Views

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

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

237 Views

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

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

146 Views

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

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