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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
$1 colon square root of 2$
$1 colon square root of 2$

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92.

If tan²x + cot²x is

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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

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

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

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

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

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

$cos space 21 degree space equals space straight x over straight y space equals space straight B over straight H$

$straight P squared space equals space straight H squared space minus space straight B squared space equals space straight y squared minus straight x squared$

$straight P space equals space square root of straight y squared minus straight x squared end root$

$cosec space 21 degree space equals space straight H over straight P space equals space fraction numerator straight y over denominator square root of straight y squared minus straight x squared end root end fraction$

$cos space 69 degree space equals space sin space 21 degree space equals space straight P over straight H space equals space fraction numerator square root of straight y squared minus straight x squared end root over denominator straight y end fraction$

$therefore space space cosec space 21 degree space minus space cos space 69 degree space equals space fraction numerator straight y over denominator square root of straight y squared minus straight x squared end root end fraction space minus space fraction numerator square root of straight y squared minus straight x squared end root over denominator straight y end fraction equals space fraction numerator straight y squared space minus space left parenthesis straight y squared minus straight x squared right parenthesis over denominator straight y square root of straight y squared minus straight x squared end root end fraction equals space fraction numerator straight y squared minus straight y squared plus straight x squared over denominator straight y square root of straight y squared minus straight x squared end root end fraction equals space fraction numerator straight x squared over denominator straight y square root of straight y squared minus straight x squared end root end fraction$

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

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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
$square root of 3$

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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°

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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:

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

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93. If then is equal to