5 A -cosec A -30- then the value of A in degrees isA- 20

The correct option is A 20sec 5A^∘ nbsp;= cosec (A 30)^∘ ∵ cosec(90^∘ θ) = sec(θ) On rearranging nbsp;the equation with one trigonometric ratio on each si ...

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Standard IX

Mathematics

Complementary Ratios

5 A ∘=cosec A...

Question

$s e c 5 A^{\circ} = c o s e c (A - 30)^{\circ}$ , then the value of A in degrees is ____ .
20

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Solution

The correct option is A 20
$s e c 5 A^{\circ} = c o s e c (A - 30)^{\circ}$

$∵$ $c o s e c (90^{\circ} - θ)$ = $s e c (θ)$

On rearranging the equation with one trigonometric ratio on each side, we get

$\Rightarrow c o s e c (90^{\circ} - 5 A) = c o s e c (A - 30)^{\circ}$

$\Rightarrow 90^{\circ} - 5 A = A - 30^{\circ}$

$\Rightarrow 6 A = 120^{\circ}$

$\Rightarrow A = 20^{\circ}$

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sec 5A∘=cosec(A−30)∘, then the value of A in degrees is ____ .20

The correct option is A 20sec 5A∘=cosec(A−30)∘ ∵ cosec(90∘−θ) = sec(θ) On rearranging the equation with one trigonometric ratio on each side, we get​ ⇒cosec(90∘−5A)=cosec(A−30)∘ ⇒90∘−5A=A−30∘ ⇒6A=120∘ ⇒A=20∘

$s e c 5 A^{\circ} = c o s e c (A - 30)^{\circ}$ , then the value of A in degrees is ____ .
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