If Ɵ be acute angle and tan (4Ɵ – 50°) = cot (50° – Ɵ), then the value of Ɵ in degrees is:

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20 Sep 2021 Trigonometry

If Ɵ be acute angle and tan (4Ɵ – 50°) = cot (50° – Ɵ), then the value of Ɵ in degrees is:

OPtion

1. 20
2. 50
3. 40
4. 30
5. 45
6. 60
7. 90
8. 75
9. 35
10. None of the above

Solution

tan (4Ɵ – 50°) = cot (50° – Ɵ)
tan (4Ɵ – 50°) = tan (90° – (50° – Ɵ))
4Ɵ – 50° = 90° – (50° – Ɵ)
4Ɵ – 50° = 90° – 50° + Ɵ
4Ɵ – 50° = 40° + Ɵ
4Ɵ – Ɵ = 40° + 50°
3Ɵ = 90°
Ɵ = 90 / 3 ° = 30°

Correct Option: 4 Best Solution (3)