Posted by **hayden** on Sunday, February 22, 2009 at 6:49pm.

cos^2 (x+a)-sin^2(a)= (cos x)(cos (2a+x))

prove using only side i worked on the left side...

- Nasty nasty proof - Precalc and trig -
**Reiny**, Sunday, February 22, 2009 at 8:10pm
I worked on both sides,

LS = (cosxcosa – sinxsina)^2 – sin^2a

= cos^2xcos^2a – 2cosxcosasinxsina + sin^2xsin^2a – sin^2a

= cos^2xcos^2a – 2cosxcosasinxsina + sin^2a(sin^2x – 1)

= cos^2xcos^2a – 2cosxcosasinxsina – sin^2acos^2x

= cos^2x(cos^2a – sin^2a) – 2cosxcosasinxsina

RS

= cosx[cos2acosx – sin2asinx]

= cosx[(cos^2a – sin^2a)cosx – 2sinacosasinx]]

= cosx[cos^2acosx – sin^2acosx – 2sinacosasinx]

= cos^2acos^2x – sin^2acos^2x - 2sinacosasinx

= cos^2x(cos^2a – sin^2a) - 2sinacosasinx

= LS

Q.E.D.

- Precalc and trig -
**hayden**, Sunday, February 22, 2009 at 8:19pm
thanks! i accidentally posted this twice

- Precalc and trig -
**hayden**, Sunday, February 22, 2009 at 8:43pm
how does

cos^2x(cos^2a – sin^2a) - 2sinacosasinx

=

cos^2x(cos^2a – sin^2a) – 2cosxcosasinxsina

- Precalc and trig -
**Reiny**, Sunday, February 22, 2009 at 11:16pm
thanks for catching that typo, it is so hard to type those complicated trig expressions without making some errors.

on RS it looks like I forgot to multiply cosx by that last term

so from

cosx[cos^2acosx – sin^2acosx – 2sinacosasinx]

= cos^2acos^2x – sin^2acos^2x - 2sinacosasinxcosx

= cos^2x(cos^2a – sin^2a) - 2sinacosasinxcosx

= LS

## Answer This Question

## Related Questions

- TRIG! - Posted by hayden on Monday, February 23, 2009 at 4:05pm. sin^6 x + cos^6...
- Math - Calculus - The identity below is significant because it relates 3 ...
- trig - it says to verify the following identity, working only on one side: cotx+...
- Trigonometry - I need to prove that the following is true. Thanks. csc^2(A/2)=...
- 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...
- Prove or Disprove - Cos(X+y)cos(x-y)= cos^2theta - sin^2theta I foiled the left ...
- tigonometry - expres the following as sums and differences of sines or cosines ...
- math - Prove that for all real values of a, b, t (theta): (a * cos t + b * sin t...
- pre-cal - Simplify the given expression........? (2sin2x)(cos6x) sin 2x and cos ...

More Related Questions