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151.
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

tan B cot A

$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 space equals space fraction numerator begin display style fraction numerator cos begin display style space end style begin display style straight A end style over denominator sin begin display style space end style begin display style straight A end style end fraction space plus space fraction numerator sin begin display style space end style begin display style straight B end style over denominator cos begin display style thin space end style begin display style straight B end style end fraction end style over denominator begin display style fraction numerator cos begin display style space end style begin display style straight B end style over denominator sin begin display style space end style begin display style straight B end style end fraction space plus space fraction numerator sin begin display style space end style begin display style straight A end style over denominator cos begin display style space end style begin display style straight A end style end fraction end style end fraction space space space space space space space space space space space space space space space space space space space space space equals fraction numerator begin display style fraction numerator cos space straight A space cos space straight B space plus space sin space straight A space sin space straight B over denominator sin space straight A space cos space straight B end fraction end style over denominator begin display style fraction numerator cos space straight A space cos space straight B space plus space sin space straight A space sin space straight B over denominator sin space straight B space cos space straight A end fraction end style end fraction space space space space space space space space space space space space space space space space space space space space space equals space fraction numerator sin begin display style space end style begin display style straight B end style begin display style space end style begin display style cos end style begin display style space end style begin display style straight A end style over denominator cos begin display style space end style begin display style straight B end style begin display style space end style begin display style sin end style begin display style space end style begin display style straight A end style end fraction space equals space tan space straight B space cot space straight A$

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