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Question

Prove that $${ (cosec\theta -cot\theta ) }^{ 2 }=\dfrac { 1-cos\theta  }{ 1+cos\theta  } $$.


Solution

LHS$$=\left(cosec\theta-cot\theta \right)^2$$

$$=\left(\dfrac{1-cos\theta}{sin\theta} \right)^2$$

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

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

$$=\dfrac{1-cos\theta}{1+cos\theta}=RHS$$

Maths

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