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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?

$21 over 29$
$29 over 21$
$20 over 29$
$29 over 20$

156.

Δ DEF is right angled at E. if $straight m space angle straight F space equals space 45 degree comma$ then what is the value of 2 sin F x cot F?

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

157.
What is the value of tan 6°. tan 36°. tan 84°. tan 54°. tan 45°?

$1 half$

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

1

$1 third$

tan 6°. tan 36°. tan 84°. tan 54°. tan 45°
= tan (90° - 84°). tan 84°. tan (90° - 54°). tan 54°. tan 45°
= cot 84°. tan 84°. cot 54°. tan 54°. 1 [As tan 45° = 1, tan θ x cot θ = 1]
= 1