Please help solve this equation?

Question

asked Sep 17, 2023 44.7k views

1 Answer

Gub · Answer 1 · 2023-09-24T07:19:22+0000

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

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.