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Trigonometric Ratios

if cosα / cos...

Question

if cosα/cosβ= n and cosα/cosβ= m then prove that (m^2+n^2)cosβ= n^2

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Solution

i think something is wrong in your question. check your question please. here in your question m and n are equal mecause you wrote it m=n=cos(alpha)/cos(bita).please watch that carefully.
but the above process is absolutely right.you just follow the process only.

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c o s α + c o s (α + β) + c o s (α + 2 β) . . . c o s (α + (n - 1) β) = \frac{c o s \frac{n β}{2}}{c o s \frac{β}{2}} {α + (n - 1) \frac{β}{2}}

\frac{cos α}{cos β} = m

\frac{cos α}{sin β} = n

(m^{2} + n^{2}) {cos}^{2} β = n^{2}

\frac{cos α}{cos β} = m, \frac{cos α}{sin β} = n,

(m^{2} + n^{2}) {cos}^{2} β = m^{2} n^{2}

\frac{cos α}{cos β} = m

\frac{cos α}{sin β} = n

(m^{2} + n^{2}) {cos}^{2} β = n^{2}

\frac{cos α}{sin β} = n

\frac{cos α}{cos β} = m

, then the value of

{cos}^{2} β

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