Question

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Answer 1

$\large \boxed{\bigg ( \: cosec \theta - cot \theta = a \bigg)} \\ \\ \large \boxed {\bigg(cot \theta = cosec \theta - a \bigg)}$

Answer 2

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$\color{violet}\huge\bold\star\underline\mathcal{Solution}\star$

» cosecø - cotø = a

» cosecø = a + cotø

squaring on both sides,

we get...

» cosec²ø = (a + cotø)²

also,cosec²ø = 1+ cot²ø

replacing cosec²ø

» 1+ cot²ø = (a+cotø)²

»1+ cot²ø = a² +2cotø(a)+cot²ø

» a²+2cotø(a)+1=0

» 2cotø(a) = -a²-1

» cotø = -(1+a²)/2a

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...#SnehaG❤