Posted by **Kinjal** on Tuesday, February 12, 2013 at 10:18am.

If sec(x+y),sec(x),sec(x-y) are in A.P. then prove that cosx= +-√2 cos y/2 where cosx and cosy are not equals to 1,

- Maths -
**Steve**, Tuesday, February 12, 2013 at 10:54am
because the difference of an AP is constant,

sec(x) - sec(x+y) = sec(x-y) - sec(x)

or, converting to cosines for ease of calculation,

cos(x+y) cos(x-y) - cos(x) cos(x-y) = cos(x) cos(x+y) - cos(x+y) cos(x-y)

2(cosx cosy - sinx siny)(cosx cosy + sinx siny) = cosx(cosx cosy + sinx siny) + cosx(cosx cosy - sinx siny)

cos^2(x)cos^2(y) - sin^2(x)sin^2(y) = cos^2(x)cosy

cos^2(x)cos^2(y) - (1-cos^2(x)-cos^2(y)+cos^2(x)cos^2(y)) = cos^2(x)cos(y)

cos^2(x)(cos(y)-1) = cos^2(y)-1

cos^2(x) = cos(y)+1

cos^2(x) = 2cos^2(y/2)

cos(x) = ±√2 cos(y/2)

## Answer This Question

## Related Questions

- Confused! Pre-Cal - Verify that each equation is an identity.. tan A= sec a/csca...
- Calculus - Q: If y=sinx/(1+tanx), find value of x not greater than pi, ...
- Integration - Intergrate ¡ì sec^3(x) dx could anybody please check this answer. ...
- Math - 1. Find y'(x) when xsecy - 3y sinx = 1 a) (3ycosx - sec y) / (xsec^2y - ...
- Trigonometry - Prove the following trigonometric identities. please give a ...
- Trig Identities - Prove the following identities: 13. tan(x) + sec(x) = (cos(x...
- Studying for math test - Multiply; then use fundamental identities to simplify ...
- Pre-Calc - Trigonometric Identities Prove: (tanx + secx -1)/(tanx - secx + 1)= ...
- TRIGONOMETRY *(MATHS) - Q.1 Prove the following identities:- (i) tan^3x/1+tan^2x...
- Calculus 2 Trigonometric Substitution - I'm working this problem: ∫ [1-tan...

More Related Questions