Question

prove that ,sin20°(3-4cos^2 70°)=√3/2.please guys solve ​

Answer 1

sin 20°(3- 4cos(270°))=3sin20°

3sin 20° = 3(√3/6)=√3/2

(proved)

Answer 2

We can put the approximate values of sin 20° and cos 70° in their places.

sin 20° = 0.342020143 = 0.342 (approx.)

cos 70° = sin 20° = 0.342020143 = 0.342 (approx.)

Therefore, sin20°(3-4cos²70°)

= 3sin20° - 4.cos²70°.sin20°

Now, putting the values of sin 20° and cos 70° in their places we get,

3×0.342 - 4×(0.342)²×0.342

= 0.866 (approx.)

= √3/2 (approx.)

If we had taken the accurate values of sin 20° and cos 70°, we would have get √3/2 accurately but since we have taken approximate values, 0.866 is approximately equal to √3/2