Prove that1 minus cotA by 1 plus cot a equals cosecA minus cotA whole square

 

Answers (1)
S safeer

To prove

 \\\frac{1-cos A}{1+cosA}=(cosecA-cotA)^2

???????\\\frac{1-cos A}{1+cosA}=\frac{(1-cosA)(1-cosA)}{(1+cosA)(1-cosA)}=\frac{(1-cosA)^2}{(1-cos^2A)}\\\\=\frac{1-2cosA+cos^2A}{sin^2A}\\\text{dividing numerator and denominator by }sin^2A\\\\\\\frac{1-cos A}{1+cosA}=\frac{1-2cosA+cos^2A}{sin^2A}=\frac{cosec^2A-2cotAcosecA+cot^2A}{1}\\\\=(cosecA-cotA)^2

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