Math, asked by jaivantprajwal, 4 days ago

Evaluate 1/1-sin alpha + 1/1+ sin alpha

Answers

Answered by Anonymous
3

To solve :-

 \dfrac{1}{1 -  \sin\alpha  } +  \dfrac{1}{1 +  \sin\alpha  }

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Solution :-

 \dashrightarrow \dfrac{1}{1 -  \sin\alpha  } +  \dfrac{1}{1 +  \sin\alpha  }

Taking LCM

{ \dashrightarrow \dfrac{1 +  \sin\alpha + 1  -   \sin\alpha}{(1 -  \sin\alpha)  (1   +  \sin\alpha)} }

Now simplifying numerator

{ \dashrightarrow \dfrac{2}{(1 -  \sin\alpha)  (1   +  \sin\alpha)} }

Apply identity in denominator (a+b) (a-b) = a² - b² where a= 1 and b = sin α

{ \dashrightarrow \dfrac{2}{(1 -  \sin ^{2} \alpha) } }

Apply formula (1 - sin²α) = cos²α

{ \dashrightarrow \dfrac{2}{( \cos^{2} \alpha) } }

Apply formula cos²α = 1/sec²α

{ \dashrightarrow 2 \sec^{2}  \alpha   }

This is the required answer.

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