Question

(cot theta + cosec theta)² = 1+cos theta / 1-cos theta​

Answer 1

solution,

Given,

$(cot\theta+cosec\theta )^2=\frac{1+cos\theta}{1-cos\theta}$

now,

LHS= $(\frac{cos\theta}{sin\theta}+\frac{1}{sin\theta})^2$

     = $(\frac{cos\theta+1}{sin\theta})^2$

    = $\frac{(cos\theta+1)^2}{sin^2\theta}$

   = $\frac{(1+cos\theta)^2}{1-cos^2\theta}$

  = $\frac{(1+cos\theta)(1+cos\theta)}{(1+cos\theta)(1-cos\theta)}$

  = $\frac{1+cos\theta}{1-cos\theta}$

        proved

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