Math, asked by chinmay2362, 3 months ago

Prove the following identity:
cos A /1+ sin A
+
1+ sin A/ cos A
= 2 sec A

Answers

Answered by sanjana121306
66

Answer:

ur answer in above picture

hope helps

Attachments:
Answered by Anonymous
97

Given

 \to \sf \dfrac{cosA}{1 + sinA}  +  \dfrac{1 + sinA}{cosA}  = 2secA

Now take LHS

 \to \sf \dfrac{cosA}{1 + sinA}  +  \dfrac{1 + sinA}{cosA}

Take LCM

 \sf  \to\dfrac{(cosA)(cosA) + (1 + sinA)(1 + sinA)}{cosA(1 +sin A)}

\sf  \to\dfrac{(cos^{2} A)+ (1 + sinA) {}^{2} }{cosA(1 +sin A)}

 \sf \to \dfrac{cos {}^{2} A + 1 + sin {}^{2}A + 2sin A}{cosA(1 +sinA) }

 \sf \to \dfrac{cos {}^{2} A + sin {}^{2}A  + 1+ 2sin A}{cosA(1 +sinA) }

 \sf \to \dfrac{1+ 1+ 2sin A}{cosA(1 +sinA) }

 \sf \to \dfrac{2+ 2sin A}{cosA(1 +sinA) }

\sf \to \dfrac{2(1+ sin A)}{cosA(1 +sinA) }

\sf \to \dfrac{2 \cancel{(1+ sin A)}}{cosA \cancel{(1 +sinA)} }

\sf \to \dfrac{2}{cosA}

\sf \to {2}{secA}

Hence Proved


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