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Mathematics

Find the value of A if

If sec 2A = cosec (A - 27°) where 2A is an acute angle, find the measure of ∠A.

Trigonometrical Ratios

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Answer

Given,

sec 2A = cosec (A - 27°)

⇒ sec 2A = sec [90° - (A - 27°)]

⇒ 2A = 90° - (A - 27°)

⇒ 2A = 90° - A + 27°

⇒ 2A = 117° - A

⇒ 3A = 117°

⇒ A = 117°3\dfrac{117°}{3}

⇒ A = 39°.

Hence, A = 39°.

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