Question

refer the above attachment and answer !
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Answer 1

Properties to be used:-

$\dashrightarrow$ $\sf (a-b)² = a²+b²-2ab$

$\dashrightarrow$ $\sf Sin²Ø = 1-Cos²Ø$

$\dashrightarrow$ $\sf a²-b² = (a+b)(a-b)$

L.H.S :-

$\implies$ $\sf (CotØ-CosecØ)²$

$\implies$ $\sf Cot²Ø+Cosec²Ø-2CotØ.CosecØ$

$\implies$ $\sf\dfrac{Cos²Ø}{Sin²Ø}+\dfrac{1}{Sin²Ø}-2×\dfrac{CosØ}{SinØ}×{1}{SinØ}$

$\implies$ $\sf\dfrac{Cos²Ø+1}{Sin²Ø}-\dfrac{2CosØ}{Sin²Ø}$

$\implies$ $\sf\dfrac{Cos²Ø+1-2CosØ}{Sin²Ø}$

$\implies$ $\sf\dfrac{(1-CosØ)²}{1-Cos²Ø}$

$\implies$ $\sf\dfrac{(1-CosØ)(1-CosØ)}{(1+CosØ)(1-CosØ)}$

$\implies$ $\sf\dfrac{1-CosØ}{1+CosØ}$ = R.H.S