If \frac{\cos\alpha }{\sin\beta}=n and{\cos \alpha}/ {\cos\beta}=m , then the value of Cos^2 \beta is

RRB NTPC Prelims Model Paper 2 with solutions

Question : 50 of 101

Marks: +1, -0

{cosα }/{sinβ}=n

and

{cos α}/ {cosβ}=m

, then the value of

Cos^2 β

Solution:

Given,

{cosα }/{sinβ}=nand {cosα} /{cosβ}=m

cos α = n sinβ cos α = m cosβ

n sinβ = m cosβ
on squaring both sides

n^2 sin^2β =m^2 cos^2β

⇒n^2 (1- cos^2β)= m^2 cos^2β

⇒n^2- n^2cos^2β = m^2 cos^2β

⇒n^2 = cos^2β (m^2 + n^2 )

∴cos^2β={n^2}/{(m^ 2+n^ 2 )}

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