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If $straight x space equals space cosec space straight theta space minus space sin space straight theta$ and $straight y equals space secθ space minus space cosθ$ , then the value of x²y² (x² + y² + 3) is

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122.

The least value of (4 sec²θ + 9 cosec²θ) is

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123.

If $0 space less or equal than space straight theta space less or equal than space space straight pi over 2 comma space space 2 straight y space cos space straight theta space equals space straight x space sin space straight theta$ and $2 straight x space sec space straight theta space minus space straight y space cosec space straight theta space equals space 3 comma$ then the value of x² + 4y² is

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124.

If $sin space 2 straight theta space equals space 1 half comma$ then the value of cos (75° - θ) is

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

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125.
If $0 space less or equal than space straight alpha space less or equal than space straight pi over 2$ and $2 space sin space straight alpha space plus space 15 space cos squared straight alpha space equals space 7 comma$ then the value of $cot space straight alpha$ is

$5 over 4$

$3 over 4$

$1 fourth$

$1 half$

$3 over 4$

$2 space sin space straight alpha space plus space 15 space cos squared straight alpha space equals space 7 rightwards double arrow space space 2 space sin space straight alpha space plus space 15 left parenthesis 1 minus sin squared straight alpha right parenthesis space equals space 7 rightwards double arrow space space 2 space sin space straight alpha space plus space 15 space minus space 15 space sin squared straight alpha space equals space 7 rightwards double arrow space space 15 space sin squared straight alpha space minus space 2 space sin space straight alpha space minus space 8 space equals space 0 rightwards double arrow space space 15 space sin squared straight alpha space minus space 12 space sinα space plus 10 space sin space straight alpha space minus space 8 space equals space 0 rightwards double arrow space space 3 space sin space straight alpha left parenthesis 5 space sin space straight alpha space minus space 4 right parenthesis space plus space 2 left parenthesis 5 space sin space straight alpha space minus space 4 right parenthesis equals space space 0 rightwards double arrow space space left parenthesis 5 space sin space straight alpha space minus space 4 right parenthesis space left parenthesis 3 space sin space straight alpha space plus space 2 right parenthesis space equals space 0$
$sin space straight alpha space equals space 4 over 5 space or space fraction numerator negative 2 over denominator 3 end fraction$
P = 4, H = 5 ∴ B = 3
$therefore space space cot space straight alpha space equals space straight B over straight P space equals space 3 over 4$

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126.

If sin (x + y) = cos {3 (x + y)}, then the value of tan {2(x + y)} is

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

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127.

The value of
(1 + sec 20° + cot 70°) (1 - cosec 20° + tan 70°) is

-1
2
1
0

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128.

If x sin³θ + y cos³θ = sin θ cos θ ≠ 0
and x sin θ - y cos θ = 0, then the value of (x² + y²) is

sin θ - cos θ
sin θ + cos θ
0
1

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129.

If $straight mu subscript straight n space equals space cos to the power of straight n straight alpha space plus space sin to the power of straight n straight alpha comma$ then the value of $2 straight mu subscript 6 space minus space 3 straight mu subscript 4 space plus space 1$ is