Question

If sec 5a cosec (A +30), where 5a is
AN acute angle
than the value of A is.​

Answer 1

Answer:

20

Step-by-step explanation:

Given, sec5A=cosec(A−30

∘

)

We know cosec(90

∘

−5A)=cosec(A−30

∘

)

⇒90

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−5A=A−30

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⇒6A=120

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So, ∠A=20

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Answer 2

$We \: have, \: \: \: \: \: \: sec \: 5A = cosec(A + {30}^{o}) \\ ⇒sec \: 5A = sec \: [{90}^{o} - (A + {30}^{o} )] \\ [∵sec \: {90}^{o} - ϑ) = cosec \: \: ϑ] \\ ⇒sec \: 5A = sec( {60}^{o} - A) \\ ⇒5A = {60}^{o} - A \\ [∵ \: 5A \: and \: ( {60}^{o} - A) \: are \: acute \: angles] \\ ⇒ \: 6A = {60}^{o} \\ ∴ \: A = {10}^{o}$