Math, asked by Anonymous, 5 months ago

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Solve this question. ​

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Answers

Answered by Spackle1017
2

Answer:

In the image.

Step-by-step explanation:

Hope this helps!

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Answered by anindyaadhikari13
3

Required Answer:-

Given to prove:

 \rm \mapsto\dfrac{ \cos(x) }{1 +  \sin(x) }  =  \dfrac{1 -  \sin(x) }{ \cos(x) }

Proof:

Here comes the proof.

Taking LHS,

 \rm \dfrac{ \cos(x) }{1 +  \sin(x) }

 \rm =  \dfrac{ \cos(x)(1 -  \sin(x))  }{(1 +  \sin(x))(1 -  \sin(x)) }

 \rm =  \dfrac{ \cos(x)(1 -  \sin(x))  }{1 -  \sin^{2} (x)}

Now, We know that,

 \rm \implies \sin^{2}(x) +  \cos^{2} (x)  = 1

 \rm \implies \cos^{2} (x)  = 1 -  \sin ^{2} (x)

Therefore, on simplifying, we get,

 \rm =  \dfrac{ \cos(x)(1 -  \sin(x))  }{\cos^{2} (x)}

 \rm =  \dfrac{1 -  \sin(x)}{\cos(x)}

= RHS (Hence Proved)

Formula Used:

  • sin²(x) + cos²(x) = 1
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