The value of 4 cos^3 40° – 3 cos 40° is (a) √3/2 (b) -1/2 (c) 1/2 (d) 1/√2

Question

The value of 4 cos³ 40° – 3 cos 40° is 

(a) \(\frac{\sqrt{3}}{2}\)

(b) \(-\frac{1}{2}\)

(c) \(\frac{1}{2}\)

(d) \(\frac{1}{\sqrt{2}}\)

Answer 1

(b) \(-\frac{1}{2}\)

4 cos³ 40° – 3 cos 40° 

= cos (3 x 40°) [∵ cos 3A = 4 cos³ A – 3 cos A] 

= cos 120° 

= cos (180° – 60°) 

= -cos 60° 

= - \(\frac{1}{2}\)