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

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

$1 half$

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

$1 third$

$1 third$

$rightwards double arrow space space space cot space 45 degree space minus space fraction numerator 1 over denominator square root of 3 end fraction cosec space 60 degree equals space 1 space minus space fraction numerator 1 over denominator square root of 3 end fraction space cross times space fraction numerator 2 over denominator square root of 3 end fraction space equals space 1 minus space 2 over 3 space equals space 1 third$