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91.
If $straight alpha space plus space straight beta space equals space 90 degree$ and $straight alpha space colon thin space straight beta space equals space 2 space colon space 1 comma$ then the ratio of $cos space straight alpha space to space cos space straight beta$ is:

$1 space colon space square root of 3$

1 : 3

$1 colon square root of 2$

$1 colon square root of 2$

$1 space colon space square root of 3$

$Let space space straight alpha space equals space 2 straight x and space straight beta space equals space straight x$

According to the question,

$straight alpha space plus space straight beta space equals space 90 degree 2 straight x space plus space straight x space equals space 90 degree space space space space space space space 3 straight x space equals space 90 degree space space space space space space space space straight x space equals space 30 degree$

$straight alpha space equals space 2 straight x space equals space 2 space cross times space 30 degree space equals space 60 degree straight beta space equals space 30 degree$

$fraction numerator cos space straight alpha over denominator cos space straight beta end fraction space equals space fraction numerator cos begin display style space end style begin display style 60 end style begin display style degree end style over denominator cos begin display style space end style begin display style 30 end style begin display style degree end style end fraction space equals space fraction numerator open parentheses begin display style 1 half end style close parentheses over denominator open parentheses begin display style fraction numerator square root of 3 over denominator 2 end fraction end style close parentheses end fraction space equals space 1 space colon space square root of 3$

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92.

If tan²x + cot²x is

98 Views

93.

If $cos space 21 degree space equals space straight x over straight y comma space$ then $cosec space 21 degree space minus space cos space 69 degree$ is equal to

$fraction numerator straight x squared over denominator straight y square root of straight y squared minus straight x squared end root end fraction$
$fraction numerator straight y squared over denominator straight x square root of straight y squared minus straight x squared end root end fraction$
$fraction numerator straight y squared over denominator straight x square root of straight x squared minus straight y squared end root end fraction$
$fraction numerator straight x squared over denominator straight y square root of straight x squared minus straight y squared end root end fraction$

59 Views

94.

If tan (5x - 10°) = cot (5y + 20°), then the value of (x + y) is

15°
16°
$22 1 half degree$
24°

71 Views

95.

θ is a positive acute angle and sin θ - cos θ = 0, then the value of sec θ + cosec θ is

2
$square root of 2$
_{$2 square root of 2$}
$3 square root of 2$

56 Views

96.

The value of $fraction numerator 2 space tan space 53 degree over denominator cot space 37 degree end fraction space minus space fraction numerator cot space 80 degree over denominator tan begin display style space end style begin display style 10 end style begin display style degree end style end fraction$ is:

61 Views

97.

The value of $cot space 17 degree open parentheses cot space 73 degree space cos squared 22 degree space plus space fraction numerator 1 over denominator cot space 17 degree space sec squared 68 degree end fraction close parentheses$ is

0
1
2
$square root of 3$

72 Views

98.

If θ > 0, be acute angle, the value of θ in degrees satisfying
$fraction numerator cos squared straight theta space minus space 3 space cosθ space plus space 2 over denominator sin squared straight theta end fraction space equals space 1$ is:

90°
30°
45°
60°

60 Views

99.

The value of (sec²45° - cot²45°) - (sin²30° + sin²60°) is

1
$2 square root of 3$
0
$fraction numerator 1 over denominator square root of 2 end fraction$

51 Views

100.

If θ is acute angle and sin (θ + 18°) = 1/2, then the value of θ in circular measure is:

$straight pi over 12 space radians$
$straight pi over 15 space radians$
$fraction numerator 2 straight pi over denominator 5 end fraction space radians$
$fraction numerator 3 straight pi over denominator 13 end fraction space radians$

45 Views

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91. If and then the ratio of is: 1 : 3