Question

Kindly solve with explaination.

Thanks.


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Answer 1

$<b><i>HEYA MATE, HERE IS UR ANSWER$

$\frac{Cos 13+ Sin 13}{Cos 13- Sin 13}$

Dividing both numerator and denominator by Cos 13.

=$\frac{cos13}{Cos 13}$+$\frac {Sin13}{Cos 13}$/$\frac {cos13}{Cos 13}$-$\frac {Sin 13}{Cos 13}$

=$\frac {1+Tan 13}{1-Tan 13}$ -----(as Sin A/Cos A =Tan A)

We can write 1= Tan 45 .

=$\frac{Tan 45 + Tan 13}{1-1×Tan 13}$

=$\frac {Tan 45+Tan 13}{1-Tan45 Tan13}$

the expression coming is similar to tangent of a compound angle .

So ,By sum formula of Tangent

Tan (45+13)

=>Tan58 =Tan A

Comparing both the sides

A=58 .

Warm regards

@laughterqueen

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Answer 2

divide numerator and denominator by cos13°,
then we have


(1+tan13°)/(1-tan13°) = tanA,


we can write it as,

(tan45°+tan13°)/(1-tan45°.tan13°) = tanA,


then it becomes

tan(45°+13°) = tanA,


tan58° = tanA,


then

A=58°