Wednesday

March 4, 2015

March 4, 2015

Posted by **samuel r. edward** on Wednesday, October 12, 2011 at 5:03am.

- trig -
**Damon**, Wednesday, October 12, 2011 at 5:26amYou have a typo which makes it kind of confusing.

tan x = n tan y

so

sin x/cos x = n sin y/cos y

n = (cos y/cos x)(sin x/sin y)

but

m = (sin x/sin y)

sin y = (1/m) sin x

cos^2 y = 1-sin^2y = 1-(1/m^2) sin^2x

so

n = (cos y / cos x)m

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

n^2 = (m^2/cos^2x) [ 1-(1/m^2)sin^2 x]

n^2 = m^2/cos^2x - sin^2x/cos^2x

n^2 cos^2x = m^2 - (1-cos^2x)

n^2 cos^2 x = m^2 - 1 + cos^2 x

(n^2-1)cos^2 x = m^2-1

so

cos^2 x = (m^2-1)/(n^2-1)

**Answer this Question**

**Related Questions**

Trig - Given: cos u = 3/5; 0 < u < pi/2 cos v = 5/13; 3pi/2 < v < ...

precalculus - For each of the following determine whether or not it is an ...

Trigonometry desperate help, clueless girl here - 2. solve cos 2x-3sin x cos 2x...

Trigonometry - 1.Solve tan^2x + tan x – 1 = 0 for the principal value(s) to two ...

Mathematics - Trigonometric Identities - Let y represent theta Prove: 1 + 1/tan^...

Trig Identities - Proving identities: 1) 1+ 1/tan^2x = 1/sin^2x 2) 2sin^2 x-1 = ...

MathsSs triG - Consider sin(x-360)sin(90-x)tan(-x)/cos(90+x) 1.A.SIMPLIFY sin(x-...

trigonometry hlp me - 6.Prove that tan y cos^2 y + sin^2y/sin y = cos y + sin y...

trig 26 - simplify to a constant or trig func. 1. sec ²u-tan ²u/cos ²v+sin ²v ...

trig help much appreciated! :)) - 1. Find the complete exact solution of sin x...