Question

Prove that costheta/1-tantheta+sintheta/1-cot theta= sintheta + costheta

Answer 1

Step-by-step explanation:

answer ...................................

Answer 2

Answer:

Step-by-step explanation:

LHS

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

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

Using the formula

$tan\theta=\frac{sin\theta}{cos\theta},cot\theta=\frac{cos\theta}{sin\theta}$

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

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

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

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

Using the identity:$a^2-b^2=(a+b)(a-b)$

$cos\theta+sin\theta=RHS$

Hence, proved

#Learns more:

https://brainly.in/question/5513889:Answered by Ayushman patra