It is given that A is an obtuse angle and cosA=-sqrt5/3.

Question

Without using calculator,find the value of cos 3A

 

 

Answer 1

cosA=-sqrt5/3.

Using formula cos3A=4cos^3A-3cosA

Substitute -sqrt5/3 for cos A

cos3A=4(-sqrt5/3)^3-3(-sqrt5/3)

            =-4(5sqrt5/3)+3sqrt5/3

             =-20sqrt5/3+3sqrt5/3

             =-17sqrt5/3

Comments

cos A = - √5/3.

cos (3A) = 4cos³ A - 3cos A

= 4(- √5/3)³ - 3(- √5/3)

= - 4(√5/3)³ + √5

= [(- 4 * 5 * √5)/27] + √5

= √5[ - 20/27 + 1]

= √5(- 20 + 27)/27

= 7√5/27.

Therefore, cos (3A) = 7√5/27.