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

$square root of 3 space cos space straight theta$
$square root of 3 space sin space straight theta$
$square root of 2 space cos space straight theta$
$square root of 2 space cos space straight theta$

189 Views

52.

If $straight x space sin space 45 degree space equals space straight y space cosec space 30 degree comma$ then $straight x to the power of 4 over straight y to the power of 4$ is equal to

181 Views

53.

fraction numerator sinA over denominator 1 plus cosA end fraction space plus space fraction numerator sin begin display style straight A end style over denominator 1 minus cosA end fraction

left parenthesis 0 degree less than space straight A space less than space 90 degree right parenthesis

2 cosec A
2 sec A
2 sin A
2 sin A

116 Views

54.

If $straight r space sin space straight theta space equals space 1 comma space space straight r space cos space straight theta space equals space square root of 3 comma$ then the value of $open parentheses square root of 3 space tan space straight theta space plus space 1 close parentheses$ is

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

141 Views

55.

If $sin squared straight alpha space plus space sin squared straight beta space equals 2 comma$ then the value of $cos open parentheses fraction numerator straight alpha space plus space straight beta over denominator 2 end fraction close parentheses$

1
-1
0
0

172 Views

56.

The value of
$cot straight pi over 20 space cot fraction numerator 3 straight pi over denominator 20 end fraction space cot space fraction numerator 5 straight pi over denominator 20 end fraction space cot fraction numerator 7 straight pi over denominator 20 end fraction space cot fraction numerator 9 straight pi over denominator 20 end fraction$ is

-1
$1 half$
0
0

191 Views

57.

If $sin space straight theta space plus space cos space straight theta space equals space 17 over 13 comma space space 0 less than straight theta less than 90 degree comma$ then the value of $sin space straight theta space minus space cos space straight theta$ is

$5 over 17$
$3 over 19$
$7 over 10$
$7 over 10$

151 Views

58.

If $tan space straight theta space. space tan space 2 straight theta space equals space 1 comma$ then the value of $sin squared 2 straight theta space plus space tan squared 2 straight theta$ is equal to

$3 over 4$
$10 over 3$
$3 3 over 4$
$3 3 over 4$

174 Views

59.

The expression $fraction numerator tan space 57 degree space plus space cot space 37 degree over denominator tan space 33 degree space plus space cot space 53 degree end fraction$ is equal to

$tan space 33 degree space cot space 57 degree$
$tan space 57 degree space cot space 37 degree$
$tan space 33 degree space cot space 53 degree$
$tan space 33 degree space cot space 53 degree$

161 Views

60.
The minimum value of sin²θ + cos²θ + sec²θ + cosec²θ + tan²θ + cot²θ is

1

3

5

5

Minimum value of sin² θ + cos²θ = 1
Minimum value of tan² θ + cot² θ = 2
Minmum value of (a cosec² θ + b sec² θ) = $left parenthesis square root of straight a space plus space square root of straight b right parenthesis squared$
∴ Minimum value of sec²θ + cosec²θ = $left parenthesis square root of 1 space plus space square root of 1 right parenthesis squared space equals space 4$
∴ Required minimum value is 1 + 2 + 4 = 7