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Mathematics

If sec (90° - 3A).cos 48° = 1 and 0 ≤ 3A ≤ 90°; find the value of angle A.

Trigonometric Identities

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Answer

Given:

sec (90° - 3A) . cos 48° = 1

⇒ cosec 3A . cos 48° = 1

⇒ 1sin 3A\dfrac{1}{\text{sin 3A}} . cos 48° = 1

⇒ sin 3A = cos 48°

⇒ sin 3A = cos (90° - 42°)

⇒ sin 3A = sin 42°

So, 3A = 42°

⇒ A = 42°3\dfrac{42°}{3}

⇒ A = 14°

Hence, A = 14°.

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