Solve the equation cot 2 ⁡ θ = 3 2 csc ⁡ θ

Question

Solve the equation      cot    2    ⁡  θ  =      3    2    csc  ⁡  θ

Laura Fletcher · Accepted Answer

Given,       cot    2    ⁡  θ  =      3    2    csc  ⁡  θwe know,       csc    2    ⁡  θ  −      cot    2    ⁡  θ  =  1    ⇒      csc    2    ⁡  θ  −  1  =      cot    2    ⁡  θSo,       csc    2    ⁡  θ  −  1  =      3    2    csc  ⁡  θ    2      csc    2    ⁡  θ  −  2  =  3  csc  ⁡  θ    2      csc    2    ⁡  θ  −  3  csc  ⁡  θ  −  2  =  0let,   csc  ⁡  θ  =  x    2      x    2    −  3  x  −  2  =  0    2      x    3    −  4  x  +  x  −  2  =  0    2  x  [  x  −  2  ]  +  1  [  x  −  2  ]  =  0    x  =  −  1      /    2   or   x  =  2    csc  ⁡  θ  =  −  1      /    2   or   csc  ⁡  θ  =  2So   csc  ⁡  θ  =      30    ∘

Solve the equation. cot^2 theta=3/2 csc theta

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