prove the following:
1+cot A/sec A=sin2 A/1-cos A
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1+cotA/secA
=1+(cosA/sinA)/(1/cosA)
=1+cos²A/sinA
=(sinA+cos²A)/sinA
sin²A/(1-cosA)
=(1-cos²A)/(1-cosA)
=(1+cosA)(1-cosA)/(1-cosA)
=1+cosA
∴, LHS≠RHS
But, if LHS
=1+cotA/cosecA
=1+(cosA/sinA)/(1/sinA)
=1+cosA
Thsn, LHS=RHS
=1+(cosA/sinA)/(1/cosA)
=1+cos²A/sinA
=(sinA+cos²A)/sinA
sin²A/(1-cosA)
=(1-cos²A)/(1-cosA)
=(1+cosA)(1-cosA)/(1-cosA)
=1+cosA
∴, LHS≠RHS
But, if LHS
=1+cotA/cosecA
=1+(cosA/sinA)/(1/sinA)
=1+cosA
Thsn, LHS=RHS
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