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cosA - sinA + 1 / cosA + sinA - 1 = cosecA + cotA
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Hi ,
LHS = ( cosA-sinA+1)/(cosA+sinA-1)
=[(cosA-sinA+1)(cosA+sinA+1)]/[(cosA+sinA-1)(cosA+sinA-1)]
= [(cosA+1)²- sin² A]/[(cosA+sinA)² -1²]
= [cos²A+2cosA+1 - sin² A]/[cos² A+sin² A+2sinAcosA -1 ]
= [ cos² A + 2cosA+ cos²A] /( 1 + 2sinAcosA-1)
= (2cos²A+ 2cosA)/(2cosAsinA)
= 2cosA( cosA + 1 ) / 2cosAsinA
= ( cosA + 1 ) / sinA
= cosA/sinA + 1/sinA
= cotA + cosecA
= RHS
I hope this helps you.
:)
LHS = ( cosA-sinA+1)/(cosA+sinA-1)
=[(cosA-sinA+1)(cosA+sinA+1)]/[(cosA+sinA-1)(cosA+sinA-1)]
= [(cosA+1)²- sin² A]/[(cosA+sinA)² -1²]
= [cos²A+2cosA+1 - sin² A]/[cos² A+sin² A+2sinAcosA -1 ]
= [ cos² A + 2cosA+ cos²A] /( 1 + 2sinAcosA-1)
= (2cos²A+ 2cosA)/(2cosAsinA)
= 2cosA( cosA + 1 ) / 2cosAsinA
= ( cosA + 1 ) / sinA
= cosA/sinA + 1/sinA
= cotA + cosecA
= RHS
I hope this helps you.
:)
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Hope this'll be helpful.....
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