Question

Prove that Cosec A- cot A ka whole square equals to 1 - cos A upon 1 + Cos A

Answer 1

Answer:

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

Step-by-step explanation:

LHS = (cosecA - cotA )²

$=\left(\frac{1}{sinA}-\frac{cosA}{sinA}\right)^{2}\\=\left(\frac{1-cosA}{sinA}\right)^{2}\\=\frac{(1-cosA)^{2}}{sin^{2}A}\\=\frac{(1-cosA)^{2}}{1-cos^{2}A}\\=\frac{(1-cosA)(1-cosA)}{(1+cosA)(1-cosA)}\\=\frac{1-cosA}{1+cosA}$

= RHS [/tex]

Therefore,

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

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