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
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
for #2, start with
LS = sin(2x + 2x)
= sin2xcos2x + cos2x sin2x
then use the double-angle formulas for each one
simplify very carefully
Answer This Question
More Related Questions
- tigonometry - expres the following as sums and differences of sines or cosines ...
- Mathematics - Trigonometric Identities - Let y represent theta Prove: 1 + 1/tan^...
- trig - Reduce the following to the sine or cosine of one angle: (i) sin145*cos75...
- Pre-Cal - 1) Verify the identity cos^2 B - sin^2 B = 2 cos^2 B -1 I know that ...
- trig - it says to verify the following identity, working only on one side: cotx+...
- Math - Guys please help me with this Trigonometry question based on De Moivre's...
- TRIG! - Posted by hayden on Monday, February 23, 2009 at 4:05pm. sin^6 x + cos^6...
- algebra - Can someone please help me do this problem? That would be great! ...
- verifying trigonometric identities - How do I do these problems? Verify the ...
- Trig! - The identities cos(a-b)=cos(a)cos(b)sin(a)sin(b) and sin(a-b)=sin(a)cos(...