Question

For the smallest positive values ​​of X and Y: tanx + tany = 2; 2cos.x cosy = 1. Solve both equations.​


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Answer 1

Answer:

The answer is x=y=56°

Step-by-step explanation:

tan45+tan45= 1+1 =2

2cos45.cos45=2×2^(1÷2)×2^(1÷2)=1

hope it will be helpful to u....

Answer 2

Step-by-step explanation:

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tanx + tany = 2

convert into sin and cos functions

sinx/cosx + Siny/cosy = 2

take L.C.M

(sinxcosy + sinycosx)/cosxcosy = 2

shift denominator to R.H.S

sinxcosy + sinycosx = 2cosxcosy

use identity:

$\tt sin(x+y)=sinxcosy + cosxsiny$

and replace the value of 2cosxcosy as 1 as it is given in the question itself.

sin(x+y) = 1

(x+y) = π/2

thus,

x= 45

y = 45

smallest positive are 45.. as if you select any other value, they would not remain smallest.