Question

1+sin/cos+cos/1+sin​

Answer 1

$\underline{\textbf{\huge{Question}}}$

$\mathbf{ \huge{\frac{1 + \sin}{ \cos } + \frac{ \cos}{1 + \sin }} }$

$\underline{\textbf{\huge{Answer}}}$

LCM of Cos and 1+sin=cos(1+sin)

$\mathbf{\huge{\frac{1 + \sin \times 1 + \sin + \cos \times \cos }{ \cos(1 + sin)} }}$

$\mathbf{\huge{\frac{(1 + \sin {}^{2}) + \cos {}^{2} }{ \cos(1 + \sin)}} }$

Using Identity=(a+b)²=a²+b²+2ab

(1+sin)=1²+2sin+sin²

$\mathbf{\huge{\frac{1 + 2 \sin + { \sin }^{2} + cos {}^{2} }{cos(1 + sin)}}}$

We know

sin²+cos²=1

$\frac{1 + { 2\sin } + 1}{ \cos(1 + sin) } \\ \\ \frac{2 + 2sin}{cos(1 + sin)} \\ \\ \frac{2\cancel{(1 + sin)}}{cos\cancel{(1 + sin)} } \\ \\ \frac{2}{cos}$

We know

1/cos=sec

2/cos=2 sec

$\boxed{\mathbf{\huge{Answer=2\:sec\theta}}}$

Answer 2

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