prove that: cotA+cosecA-1/cotA-cosecA+1=1+cosA/sinA
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Hii friend,
CotA + CosecA-1/CotA - CosecA +1 = 1+CosA/SinA.
We have,
LHS = CotA+CosecA-1/CotA-CosecA+1
=> (CosecA+CotA)-(Cosec²A-Cot²A)/(CotA-CosecA +1) [ Cosec² theta-Cot²theta = 1)
=> (CosecA+CotA)[1-(CosecA-CotA)/ ( CotA-CosecA+1).
=> (CosecA-CotA) ( CotA-CosecA+1)/(CotA-CosecA+1).
=> (CosecA+CotA)
=> (1/SinA + CosA/SinA)
=> (1+CosA/SinA) = RHS
Hence,
LHS = RHS = 1+CosA/SinA..... PROVED......
HOPE IT WILL HELP YOU... :-)
CotA + CosecA-1/CotA - CosecA +1 = 1+CosA/SinA.
We have,
LHS = CotA+CosecA-1/CotA-CosecA+1
=> (CosecA+CotA)-(Cosec²A-Cot²A)/(CotA-CosecA +1) [ Cosec² theta-Cot²theta = 1)
=> (CosecA+CotA)[1-(CosecA-CotA)/ ( CotA-CosecA+1).
=> (CosecA-CotA) ( CotA-CosecA+1)/(CotA-CosecA+1).
=> (CosecA+CotA)
=> (1/SinA + CosA/SinA)
=> (1+CosA/SinA) = RHS
Hence,
LHS = RHS = 1+CosA/SinA..... PROVED......
HOPE IT WILL HELP YOU... :-)
hi
sister
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