Turn on thread page Beta
    • Thread Starter
    Offline

    3
    ReputationRep:
    Can anyone help me with this trig identity proof! Attempted it several times from scratch and just can't get anywhere! Thanks

    1 + 2cos2x + cos4x = 4cos^2xcos2x
    Offline

    2
    ReputationRep:
    Three steps: (1) rewrite the LHS in terms of cos(x); (2) pull out [cos(x)]^2 as a factor; (3) show that the other factor equals 4 cos(2x).

    cos(2x) = 2 [cos(x)]^2 - 1.

    cos(4x)
    = 2 [cos(2x)]^2 - 1
    = 2 (2 [cos(x)]^2 - 1)^2 - 1
    = 8 [cos(x)]^4 - 8 [cos(x)]^2 + 1.

    So
    1 + 2 cos(2x) + cos(4x)
    = 8 [cos(x)]^4 - 4 [cos(x)]^2
    = 4 [cos(x)]^2 * (2 [cos(x)]^2 - 1)
    = 4 [cos(x)]^2 * cos(2x).
 
 
 
Poll
“Yanny” or “Laurel”

The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

Write a reply...
Reply
Hide
Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.