if 2cosA+sinA =1 then 7cosA+ 6sinA is equal to - Maths - Trigonometric Functions

Question

if 2cosA+sinA =1 then 7cosA+ 6sinA is equal to

Devesh Kumar · Accepted Answer

If 2cosA+sinA =1 then 7cosA+ 6sinA=?2cosA+sinA =1⇒2cosA2=1-sinA 2⇒4cos2A=1+sin2A -2sinA⇒41-sin2A=1+sin2A -2sinA⇒4-4sin2A=1+sin2A -2sinA⇒5sin2A-2sinA -3=0⇒5sinAsinA-1 +3sinA-1 =0⇒sinA-1 5sinA+3=0⇒sinA=1    & sinA=-35when sinA=1⇒cosA=1-sin2A =0  …1  & when sinA=-35cosA=1--352=1625=±45…2Using eq 1⇒7cosA+ 6sinA=70+ 61=6          AnswerUsing eq 1⇒7cosA+ 6sinA=745+ 6-35=285-185=105=2