Question

if cosec^2(x/2) - cot^2(x+30/3)=cot 45, then find value of x​

Answer 1

$\textbf{Given:}$

$cosec^2(\frac{x}{2})-cot^2(\frac{x+30}{3})=cot\,45$

$\implies\,cosec^2(\frac{x}{2})-cot^2(\frac{x+30}{3})=1$

$\implies\,cosec^2(\frac{x}{2})=1+cot^2(\frac{x+30}{3})$

$\text{Using,}\boxed{\bf\,cosec^2A=1+cot^2A}$

$\implies\,cosec^2(\frac{x}{2})=cosec^2(\frac{x+30}{3})$

$\implies\,\frac{x}{2}=\frac{x+30}{3}$

$\implies\,3x=2x+60$

$\implies\,3x-2x=60$

$\implies\,x=60$

$\therefore\textbf{The value of x is 60}$

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Answer 2

Answer:

mate here is your answer