Prove the identity 

Asked by Anish | 16th Jun, 2018, 03:25: PM

Expert Answer:

cosx (tanx + 2)(2tanx + 1) = 2secx + 5sinx
 
begin mathsize 16px style LHS space equals space cosx left parenthesis tanx space plus space 2 right parenthesis space left parenthesis 2 tanx space plus space 1 right parenthesis
equals cosx left parenthesis 2 tan squared straight x space plus space tanx space plus space 4 tanx space plus space 2 right parenthesis
equals cosx open parentheses 2 cross times fraction numerator sin squared straight x over denominator cos squared straight x end fraction space plus 5 space tanx plus space 2 close parentheses
equals cosx open parentheses fraction numerator 2 sin squared straight x plus 5 tanxcos squared straight x plus 2 cos squared straight x over denominator cos squared straight x end fraction close parentheses
equals fraction numerator 2 sin squared straight x plus 5 begin display style fraction numerator sinxcos squared straight x over denominator cosx end fraction end style plus 2 cos squared straight x over denominator cosx end fraction
equals fraction numerator 2 sin squared straight x plus 2 cos squared straight x plus 5 begin display style sinxcosx end style over denominator cosx end fraction
equals fraction numerator 2 plus 5 sinxcosx over denominator cosx end fraction
equals 2 over cosx plus fraction numerator 5 sinxcosx over denominator cosx end fraction
equals 2 secx plus 5 sinx equals space RHS
end style = 2secx + 5sinx

Answered by Sneha shidid | 18th Jun, 2018, 10:07: AM