Question

(cosec theta -cot theta.) (cosec theta -cot theta.)=1-costheta/1+costheta

Answer 1

Answer:

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

Step-by-step explanation:

$Formula\: used:\\\\cosec^2A-cot^2A=1\\\\(cosecA-cotA)(cosecA+cotA)=1\\\\cosecA-cotA=\frac{1}{cosecA+cotA}$

$Now\\\\(cosec\theta-cot\theta)(cosec\theta-cot\theta)\\\\=(cosec\theta-cot\theta)(\frac{1}{cosec\theta+cot\theta})\\\\=\frac{cosec\theta-cot\theta}{cosec\theta+cot\theta}\\\\=\frac{\frac{1}{sin\theta}-\frac{cos\theta}{sin\theta}}{\frac{1}{sin\theta}+\frac{cos\theta}{sin\theta}}\\\\=\frac{\frac{1-cos\theta}{sin\theta}}{\frac{1+cos\theta}{sin\theta}}\\\\=\frac{1-cos\theta}{1+cos\theta}$