Find the value of \(\frac{1}{sin10°} - 4\, sin70°.\)

1.	Find the value of \(\frac{1}{sin10°} - 4\, sin70°.\)
Answer» sin(3 × 10°) = sin(30°) = \(\frac{1}{2}\) ⇒ 3 sin10° - 4 sin³10° = \(\frac{1}{2}\) ⇒ 8 sin³10° - 6 sin10° + 1 = 0 After solving this polynomial in sin10°, we get ⇒ sin10° = 0.17365 sin70° = sin(10° + 60°) = sin10° cos60° + cos10° sin60° = 0.17365 × \(\frac{1}{2}\) + 0.9848 × \(\frac{\sqrt3}{2}\) = 0.086825 + 0.852868 = 0.93693 \(\frac{1}{sin 10°}\) - 4 sin70° = \(\frac{1}{0.17365} - 4(0.93693)\) = 5.75871 - 3.74772 = 2.01099 (2.011 Approx)

Answer»

sin(3 × 10°) = sin(30°) = \(\frac{1}{2}\)

⇒ 3 sin10° - 4 sin³10° = \(\frac{1}{2}\)

⇒ 8 sin³10° - 6 sin10° + 1 = 0

After solving this polynomial in sin10°, we get

⇒ sin10° = 0.17365

sin70° = sin(10° + 60°)

= sin10° cos60° + cos10° sin60°

= 0.17365 × \(\frac{1}{2}\) + 0.9848 × \(\frac{\sqrt3}{2}\)

= 0.086825 + 0.852868

= 0.93693

\(\frac{1}{sin 10°}\) - 4 sin70° = \(\frac{1}{0.17365} - 4(0.93693)\)

= 5.75871 - 3.74772

= 2.01099 (2.011 Approx)

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