Question

30 big anfon Ah COSA +AsinA =2seca
COSA
HSINA​

Answer 1

Solution

$\tt \implies \dfrac{cosA}{1 + sinA} + \dfrac{1 + sinA}{cosA} = 2secA$

Now Take

$\tt \implies \dfrac{cosA}{1 + sinA} + \dfrac{1 + sinA}{cosA}$

Taking LCM

$\tt \implies \dfrac{(cosA)(cosA) + (1 + sinA)(1 + sinA)}{(1 + sinA)(cosA)}$

$\tt \implies \: \dfrac{cos^{2} A + (1 + sinA)^{2} }{cosA + sinAcosA}$

$\tt \implies \: \dfrac{cos^{2}A + 1 + sin ^{2} + 2sin A}{cosA (1+ sinA)}$

$\tt \implies \: \dfrac{1 + 1 + 2sin A}{cosA (1+ sinA)}$

$\tt \implies \: \dfrac{2 + 2sin A}{cosA (1+ sinA)}$

$\tt \implies \: \dfrac{2( 1+ sin A)}{cosA (1+ sinA)}$

$\tt \implies \: \dfrac{2 \cancel{( 1+ sin A)}}{cosA \cancel{(1+ sinA)}}$

$\tt \implies \: \dfrac{2}{cosA} = 2secA$

Hence Proved