prove that Cos A - Sin A + 1 ÷ Cos A + Sin A - 1 = Cosec A + Cot A
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LHS=cosA−sinA+1cosA+sinA−1
=sinA(cosA−sinA+1)sinA(cosA+sinA−1)
=sinAcosA−sin2A+sinAsinA(cosA+sinA−1)
=sinAcosA+sinA−(1−cos2A)sinA(cosA+sinA−1)
=sinA(cosA+1)−(1−cosA)(1+cosA)sinA(cosA+sinA−1)
=(1+cosA)(sinA+cosA−1)sinA(cosA+sinA−1)
=(1+cosA)(sinA+cosA−1)sinA(cosA+sinA−1)
=1sinA+cosAsinA
=cscA+cotA=RHS
Proved
=sinA(cosA−sinA+1)sinA(cosA+sinA−1)
=sinAcosA−sin2A+sinAsinA(cosA+sinA−1)
=sinAcosA+sinA−(1−cos2A)sinA(cosA+sinA−1)
=sinA(cosA+1)−(1−cosA)(1+cosA)sinA(cosA+sinA−1)
=(1+cosA)(sinA+cosA−1)sinA(cosA+sinA−1)
=(1+cosA)(sinA+cosA−1)sinA(cosA+sinA−1)
=1sinA+cosAsinA
=cscA+cotA=RHS
Proved
koushik18:
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bro there is division not addition see the question again
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