Find the value of #lamda, (3-tan^2(π/7)#) /# 1-tan^2#(π/7)# = #lambda cos(π/7)#?

1 Answer
Shiva Prakash M V
Mar 6, 2018

#lambda=sec^2(pi/7)-2#

Explanation:

#lambda=?#
Given:
#(3-tan^2(pi/7))/(1-tan^2(pi/7))=lambdacos(pi/7)#
#tan^2theta=1+sec^2theta#
#costheta=1/sectheta#
If #theta=pi/7#
then
#(3-tan^2(pi/7))/(1-tan^2(pi/7))=lambdacos(pi/7)#
becomes
#(3-tan^2theta)/(1-tan^2theta)=lambdacostheta#
#(3-(1+sec^2theta))/(1-(1+sec^2theta))=lambda/sectheta#
#(2-sec^2theta)/(-sec^2theta)=lambda/sectheta#
#(2-sec^2theta)=-lambda#
#lambda=-(2-sec^2theta)#
#lambda=sec^2theta-2#
#theta=pi/7#
Thus,
#lambda=sec^2(pi/7)-2#

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