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Mathematics

When 0° < A < 90°, solve the following equations :

(i) sin 3A = cos 2A

(ii) tan 5A = cot A

Trigonometrical Ratios

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Answer

(i) Given,

⇒ sin 3A = cos 2A

⇒ sin 3A = sin (90° - 2A)

⇒ 3A = 90° - 2A

⇒ 5A = 90°

⇒ A = 905\dfrac{90}{5}

⇒ A = 18°.

Hence, A = 18°.

(ii) Given,

⇒ tan 5A = cot A

⇒ tan 5A = tan (90° - A)

⇒ 5A = 90° - A

⇒ 6A = 90°

⇒ A = 906\dfrac{90}{6}

⇒ A = 15°.

Hence, A = 15°.

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