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Answer:
Step-by-step explanation:
LHS
Sina-cosa+1/sina+cosa-1
Divide numerator and denominator by cosa
Tana-1+seca/tana+1-seca
Tana-1+seca/tana-seca+sec^2a - tan^2 a
(By identity)
Tana-1+seca/(seca-tana)(tana-1+seca)
(Taking common out)
Numerator and denominator gets cancelled leaving 1/seca-tana
=RHS
Therefore, LHS = RHS
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Answer:
LHS = (sinA-cosA+1)/(sinA+cos-1) = (1 + sinA) (1 - sinA)/cos A(1 - sinA) = 1 - sin2A/cos A(1 - sinA) = cos2A/cos A(1 - sinA) = cosA/(1 - sinA) = 1/ (1/cosA - sinA/cosA) = 1/(secA - tanA) = RHS Hence Proved
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