Question

prove that :sinA/secA+tanA-1+ cosA/ cosecA+cotA-1=1​

Answer 1

Answer:   sinA/secA+tanA-1+ cosA/ cosecA+cotA-1=1​

= sinA/[(1/cosA)+(sinA/cosA)-1] + cosA/[(1/sinA)+(cosA/sinA)-1]

= sinA/[(1+sinA-cosA)/cosA] + cosA/[(1+cosA-sinA)/sinA]

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

= sinA*cosA[1/(1+sinA-cosA) +1/(1+cosA-sinA)]

= sinA*cosA[(1+cosA-sinA+1+sinA-cosA)/(1+sinA-cosA)(1+cosA-sinA)]

= sinA*cosA[2/(1+cosA-sinA+sinA+sinAcosA-sin2A-cosA-cos2A+cosAsinA)]

sinA*cosA[2/(1-sin2A-cos2A+2sinAcosA)]

= sinAcosA[2/(1-(sin2A+cos2A)+2sinAcosA)]

= sinAcosA[2/(1-1+2sinAcosA)]      (since sin2A+cos2A=1)

= sinAcosA[2/2sinAcosA]

=sinAcosA*1/sinAcosA

= 1  PROVED

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