If 4 sin theta = 3 cos theta then find 4 cos^2 theta - 3 sin^2 theta +2?

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Answer 1 · 2018-02-25T04:11:07

Given #4 sin theta = 3 cos theta#

#=>tantheta=3/4#

Now # 4 cos^2 theta - 3 sin^2 theta +2#

#=( 4 cos^2 theta - 3 sin^2 theta +2)/(cos^2theta+sin^2theta)#

#=( (4 cos^2 theta)/cos^2theta - (3 sin^2 theta)/cos^2theta +2/cos^2theta)/(cos^2theta/cos^2theta+sin^2theta/cos^2theta)#

#= (4 - 3 tan^2theta +2sec^2theta)/(1+tan^2theta)#

#= (4 - 3 tan^2theta +2+2tan^2theta)/(1+tan^2theta)#
#= (6 - tan^2theta )/(1+tan^2theta)#

#= (6 - (3/4)^2 )/(1+(3/4)^2)#

#= (6*1 6 - 9 )/(16+9)#

#=87/25#