Question

Show that 1/(cosecA-cotA) - 1/sinA = 1/sinA - 1/(cosecA+cotA).
No spam please help me....

Answer 1

Step-by-step explanation:

(1/cosecA-cotA)-(1/sinA)

={1/(1/sinA-cosA/sinA)}-(1/sinA)

=[1/{(1-cosA)/sinA}]-(1/sinA)

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

=(sin²A-1+cosA)/sinA(1-cosA)

={(1-cos²A)-(1-cosA)}/sinA(1-cosA)

={(1+cosA)(1-cosA)-(1-cosA)}/sinA(1-cosA)

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

=cosA/sinA

=cotA

RHS

(1/sinA)-(1/cosecA+cotA)

=(1/sinA)-{1/(1/sinA+cosA/sinA)}

=(1/sinA)-1/{(1+cosA)/sinA}

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

=(1+cosA-sin²A)/sinA(1+cosA)

={1+cosA-(1-cos²A)}/{sinA(1+cosA)}

={(1+cosA)-(1+cosA)(1-cosA)}/{sinA(1+cosA)}

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

=cosA/sinA

=cotA

LHS = RHS

hence proved

Answer 2

Step by step explation:

LHS=RHS (verified)..

Please mark me as the brain list and follow me