Math, asked by saraswatankita74, 1 month ago

cosA-SinA+1/cosA+SinA+1=1/cosecA-cotA

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Lets take the LHS =

(cosA-sinA)+1/(cosA+sinA)-1

taking conjugate

(cosA-sinA)+1/(cosA+sinA)-1 × (cosA+sinA)+1/(cosA+sinA)+1

multiplying we get

=cos2A-sin2A+2cosA+1/2sinAcosA

=cos2A-sin2A+2cosA+sin2A+cos2A/2sinAcosA

on solving we get

=2cos2A+2cosA/2sinAcosA

=cosA+cos2A/sinAcosA

we can alsom write in the form of

cosA/sinAcosA +cos2A/sinAcosA

on solving we get

CosecA+cotA =R.H.S

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