Question

cos theta/1-tan theta + sin theta/1-cot theta

Answer 1

Check out this
Hope this helps

Answer 2

Answer:

$\frac{cos\theta}{1-tan\theta}+\frac{sin\theta}{1-cot\theta}=cos\theta+sin\theta$

Step-by-step explanation:

$\frac{cos\theta}{1-tan\theta}+\frac{sin\theta}{1-cot\theta}$

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

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

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

$=\frac{cos^{2}\theta -sin^{2}\theta}{cos\theta-sin\theta}$

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

After cancellation,we get

=$cos\theta+sin\theta$

Therefore,

$\frac{cos\theta}{1-tan\theta}+\frac{sin\theta}{1-cot\theta}=cos\theta+sin\theta$

•••♪