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Alex
1 year ago
12

Please help solve this equation?

Mathematics
1 answer:
finlep [7]1 year ago
5 0

{ \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.

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