Solve the following equations: sin 3A = cos 2A

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

(i) sin 3A = cos 2A
(ii) tan 5A = cot A

Answer :

(i) sin 3A = cos 2A

⇒ sin 3A = sin (90° – 2A)

3A = 90° – 2A

⇒ 3 A + 2A = 90°

⇒ 5A = 90°

∴ A = 90°/5 = 18°

⇒  tan 5A = cot A

⇒ tan 5A = tan (90° – A)

5A = 90°- A

⇒ 5A + A = 90°

⇒ 6A = 90°

∴ A = 90°/6 = 15°

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