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What is the simplified value of $fraction numerator cot space straight A space plus space tan space straight B over denominator cot space straight B space plus space tan space straight A end fraction ?$

tan B cot A
tan A cot B
tan A tan B
cot A cot B

152.

What is the simplified value of $open parentheses fraction numerator 1 over denominator cosec space straight A space plus space cot space straight A end fraction close parentheses squared ?$

sec A + tan A
$fraction numerator open parentheses 1 space minus space cos space straight A close parentheses over denominator left parenthesis 1 space plus space cos space straight A right parenthesis end fraction$
$fraction numerator left parenthesis 1 minus cosec space straight A right parenthesis over denominator left parenthesis 1 space plus space cosec space straight A right parenthesis end fraction$
sin A

153.

If cos²θ - sin θ = 1/4, then what is the value of sin θ?

-1
1/2
1
3/2

154.

What is the value of $cot space 45 degree space minus space open parentheses fraction numerator 1 over denominator square root of 3 end fraction close parentheses space cosec space 60 degree$ ?

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

155.
If $cot space straight theta space equals space 21 over 20 comma$ then what is the value of cosec θ?

$21 over 29$

$29 over 21$

$20 over 29$

$29 over 20$

$29 over 20$

$cot space straight theta space equals space 21 over 20 space equals space straight B over straight P$
$space space space straight H squared space equals space straight P squared space plus space straight B squared space space space space space space space space space space space equals space left parenthesis 20 right parenthesis squared space plus space left parenthesis 21 right parenthesis squared space space space space space space space space space space space equals space 400 space plus space 441 space equals space 841 therefore space space straight H space equals space square root of 841 space equals space 29$
$cosec space straight theta space equals space straight H over straight P space equals space 29 over 20$