Show that SinA/(secA+tanA-1) + cosA/(cosecA+cotA-1) = 1
Show that SinA/(secA+tanA-1) + cosA/(cosecA+cotA-1) = 1
Shaikh Ashraf , 8 Years ago
Grade 10
10 grade maths> Show that SinA/(secA+tanA-1) + cosA/(cose...
1 Answers
Arun
sinA/(1/cosA+sinA/cosA-1)+cosA/(1/sinA+cosA/sinA-1)
=sinA/{(1+sinA-cosA)/cosA}+cosA/{(1+cosA-sinA)/sinA}
=sinAcosA/(1+sinA-cosA)+sinAcosA/(1+cosA-sinA)
=sinAcosA[(1+cosA-sinA+1+sinA-cosA)/(1+sinA-cosA)(1+cosA-sinA)]
=2sinAcosA/(1+sinA-cosA+cosA+sinAcosA-cos²A-sinA-sin²A+sinAcosA)
=2sinAcosA/{1+2sinAcosA-(sin²A+cos²A)}
=2sinAcosA/(1+2sinAcosA-1)
=2sinAcosA/2sinAcosA
=1 (Proved)
=sinA/{(1+sinA-cosA)/cosA}+cosA/{(1+cosA-sinA)/sinA}
=sinAcosA/(1+sinA-cosA)+sinAcosA/(1+cosA-sinA)
=sinAcosA[(1+cosA-sinA+1+sinA-cosA)/(1+sinA-cosA)(1+cosA-sinA)]
=2sinAcosA/(1+sinA-cosA+cosA+sinAcosA-cos²A-sinA-sin²A+sinAcosA)
=2sinAcosA/{1+2sinAcosA-(sin²A+cos²A)}
=2sinAcosA/(1+2sinAcosA-1)
=2sinAcosA/2sinAcosA
=1 (Proved)
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