Question

Please help solve this equation?

Answer 1

${ \red{ \bold{cos \: y \: }}}$

Step-by-step explanation:

${ \green{ \tt{ \frac{1 \: + \: \cos \: y \: }{1 \: + \: \sec \: y \: }}}} \: → {eq}^{n} (1)$

But, as you know that

${ \blue{ \tt{sec \: y \:}}} = { \green{ \tt{\frac{1}{ \ \cos \: y }}}}$

Then the equation (1) becomes

${ \green{ \tt{ \frac{1 \: + \: cos \: y }{1 \: + \: \frac{1}{cos \: y} }}}} \:$

Multiply Numerator and Denominator by $\frac{cos \: y}{cos \: y}$

then,

${ \green{ \tt{( \frac{cos \: y}{cos \: y})}}} \: { \green{ \tt{ \frac{1 \: + \: cos \: y}{1 \: + \: \frac{1}{cos \: y}}}}}$

$= { \green{ \tt{ \frac{cos \: y \: + \: {cos}^{2} \: y }{cos \: y \: + \: 1 }}}}$

take cos y as common, then

${ \green{ \tt{cos \: y}}} \: { \green{ \tt( \frac{1 \: + \: cos \: y}{cos \: y \: + \: 1} )}}$

Here, (1+cos y/cos y + 1) gets cancelled.

Then the remaining answer is cos y.