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Verify the identity: cos(-?)/1 + sin(-?) = sec? + tan?
Solution
cos(-x)=cosx and sin(-x)=-sinx
So LHS=cosx/1-sinx
=(cosx)(1+sinx)/(1-sinx)(1+sinx)
=cosx(1+sinx)/(1-sin^2x)
=cosx(1+sinx)/cos^2x
=1+sinx/cosx
RHS=secx+tanx=1/cosx+sinx/cosx
=1+sinx/cosx
So LHS=RHS
Hence the identity is correct

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  • 1. Verify the identity: cos(-?)/1 + sin(-?) = sec? + tan? Solution cos(-x)=cosx and sin(-x)=-sinx So LHS=cosx/1-sinx =(cosx)(1+sinx)/(1-sinx)(1+sinx) =cosx(1+sinx)/(1-sin^2x) =cosx(1+sinx)/cos^2x =1+sinx/cosx RHS=secx+tanx=1/cosx+sinx/cosx =1+sinx/cosx So LHS=RHS Hence the identity is correct