Question

2-cosec²a/cosec²a+2 cota = sina-cosa/sina+cosa

Answer 1

Step-by-step explanation:

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Answer 2

By the given explanation, It is proven that 2-cosec²a/cosec²a+ 2 cot a = sin a - cos a/ sin a+cos a  

Given:

2-cosec²a/cosec²a+ 2 cot a = sin a - cos a/ sin a+cos a  

To find:

Prove the given statement

Solution:

Given that

$\frac{2 -csc^{2} a}{csc^{2} a+ 2 cot a } = \frac{sin a - cos a}{sin a+cos a}$  

Take L H S   $\frac{2 -csc^{2} a}{csc^{2} a+ 2 cot a }$  

=> $\frac{2 - \frac{1}{sin^{2}a} }{\frac{1}{sin^{2} a} + 2 \frac{cos a}{sin a} }$       [ since csc = 1/sin ]

=> $\frac{2sin^{2}a - 1}{ 1 + 2 cos a sin a} }$    

=>  $\frac{2sin^{2}a - sin^{2} a - cos^{2} a }{ sin^{2} a + cos^{2} a + 2 cos a sin a} }$     [ take 1 = sin²a + cos² a ]

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

=> $\frac{ (sin a - cos a)(sin a + cos a) }{ (sin a + cos a)^{2} }$     [ Use (a² - b²) = (a + b) (a - b) ]

=> $\frac{ (sin a - cos a) }{ (sin a + cos a) }$  = RHS

Here LHS = RHS

Therefore,

By the given explanation, It is proven that 2-cosec²a/cosec²a+ 2 cot a = sin a - cos a/ sin a+cos a  

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