Question

8 cos^3 20degree -6 cos 20 degree

Answer 1

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Answer 2

Answer:

1

Step-by-step explanation:

Given:- 8 cos³ 20° - 6 cos 20°

To Find:- The value of the above expression.

Solution:-

According to the trigonometric formulas, we know that

                        cos3A = 4cos³A - 3cosA

                    ⇒ 4 cos³A = cos 3A + 3 cos A          --------- ( 1 )

The given expression is

8 cos³ 20° - 6 cos 20°

= 2 (4 cos³ 20°) - 6 cos20°

= 2 (cos 3(20°) + 3 cos20°) - 6 cos20°     [Acc. to the equation ( 1 )]

= 2 (cos 60° + 3 cos 20°) - 6 cos20°

= 2 cos60° + 6 cos20° - 6 cos20°

= 2 cos 60°

= 2 × $\frac{1}{2}$     [∵ cos 60° = $\frac{1}{2}$]

= 1

Therefore, 8 cos³20° - 6 cos20° = 1.

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