Question

Please help solve this equation?

Answer 1

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

Explanation:

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

But, as you know that

`{ \blue{ \tt{sec \: y \:}}} = { \green{ \tt{(1)/( \ \cos \: y )}}}`

Then the equation (1) becomes

`{ \green{ \tt{ (1 \: + \: cos \: y )/(1 \: + \: (1)/(cos \: y) )}}} \:`

Multiply Numerator and Denominator by
`(cos \: y)/(cos \: y)`

then,

`{ \green{ \tt{( (cos \: y)/(cos \: y))}}} \: { \green{ \tt{ (1 \: + \: cos \: y)/(1 \: + \: (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( (1 \: + \: cos \: y)/(cos \: y \: + \: 1) )}}`

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

Then the remaining answer is cos y.