If sin 3x = 1 and 0° ≤ 3x ≤ 90°

If sin 3x = 1 and 0° ≤ 3x ≤ 90°, find the values of

(i) sin x

(ii) cos 2x

(iii) tan² x – sec² x.

Answer :

sin 3x = 1

sin 90° = 1

sin 3x = sin 90°

3x = 90

⇒ x = 90/3

⇒ x = 30°

(i) sin x = sin 30° = 1/2

(ii) cos 2x = cos 2 × 30 = cos 60° = 1/2

(iii) tan² x – sec² x = tan² 30° – sec² 30°

= (1/√3)² – (2/√3)²

= 1/3 – 4/3

= (1 – 4)/3

= – 3/3

= -1

Hence, tan² x – sec² x = – 1.

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