Question

Evaluate 3sin30-4cos^3 60?

Answer 1

We have to evaluate
3. sin 30° - 4. cos³ 60°
Solution:
3. sin 30° - 4. cos³ 60° = 3. sin 30° - 4. (cos 60°)³  
                  [ ∵ cos³ Ф = (cos Ф)³ ]
3. sin 30° - 4. cos³ 60° = 3. (1 / 2) - 4. (1 / 2) ³
            [ ∵ sin 30° = 1/2 , cos 60° = 1/2 ]
3. sin 30° - 4. cos³ 60° = 3 / 2 - 4. (1 / 8)
3. sin 30° - 4. cos³ 60° = 3 / 2 - 4 / 8
3. sin 30° - 4. cos³ 60° = 3 / 2 - 1 / 2
3. sin 30° - 4. cos³ 60° = (3 - 1) / 2
3. sin 30° - 4. cos³ 60° = 2 / 2
3. sin 30° - 4. cos³ 60° = 1
which is the required answer.
Hopefully it's helpful to you.
Thanks.

Answer 2

Question :

3sin30° - 4cos³ 60°

= 3sin30° - 4(cos 60°)³

= 3(1/2) - 4(1/2)³

[ Sin 30°= 1/2, cos 60° = 1/2]

= 3/2 - 4(1/8)

= 3/2 - 4/8

= (3×4 - 4×1)/8

= (12-4)/8

= 8 /8

3sin30° - 4cos³ 60°= 1

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Hope this will help you...