Posted by **PDF** on Monday, August 27, 2012 at 2:22am.

Verify that following are identities:

1. cos 3t = 4 cos³ t-3 cos t

2. sin 4x = 8 sin x cos³ x-4 x cos x

(use a double-angle identity)

- trigonometry -
**Reiny**, Monday, August 27, 2012 at 8:01am
1.

LS = cos 3t

= cos(2t + t)

= cos2tcost - sin2tsint

= (2cos^2 t - 1)(cost) - 2sintcostsint

= 2cos^3 t - cost - 2sin^2 t cost

= 2cos^3 t - cost - 2(1 - cos^2 t)cost

= 2cos^3 t - cost - 2cost + 2cos^3 t

= 4cos^3 t - 3cost

= RS

for #2, start with

LS = sin(2x + 2x)

= sin2xcos2x + cos2x sin2x

then use the double-angle formulas for each one

simplify very carefully

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