Question

(Cosec theta-cot theta)²=1-cos Theta/1+cos theta

Answer 1

Answer:

I hope you guys will find it useful pls mark me as brainliest

Step-by-step explanation:

Answer 2

Answer:

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

Step-by-step explanation:

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

/*

$we\: know \: that \\i) cosec\theta =\frac{1}{sin\theta}\\ii)cot\theta = \frac{cos\theta}{sin\theta}$

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

$By \: trigonometric \: identity : \\\boxed{sin^{2}\theta = 1-cos^{2}\theta}$

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

After cancellation, we get

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

•••♪