Chemistry, asked by Anonymous, 4 months ago

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

Answers

Answered by kritanuchatterjee280
2

Answer:

PROVED

Explanation:

\frac{cosA}{1+sinA} + \frac{1+sinA}{cosA} = 2 secA\\

LHS

\frac{cosA}{1+sinA}+ \frac{1+sinA}{cosA} \\\frac{cos^2A+(1+sinA)^2}{(1+sinA)cosA}\\\frac{cos^2A + 1+sin^2A+2sinA}{cosA(1+sinA)}(since, a^2+b^2+2ab = (a+b)^2\\\frac{1+1+2sinA}{cosA(1+sinA)} (since, sin^2A + cos^2A = 1)\\\frac{2+2sinA}{cosA(1+sinA)}\\\frac{2(1+sinA)}{cosA(1+sinA)}\\\frac{2}{cosA}\\2secA (sec A =\frac{1}{cosA})

thus, LHS=RHS(hence,proved)

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