Question

Sin( 2x -20)= cos ( 2y+20), then tan (x+y )=?

Answer 1

Answer:

$\red {Value \: of \: tan(x+y) } \green {= 1}$

Step-by-step explanation:

$Given \: sin(2x-20) = cos (2y+20)$

$\implies sin(2x-20) = Sin [ 90-(2y+20)]$

$\boxed { \pink { cos A = sin (90 - A) }}$

$\implies 2x - 20 = 90 -(2y+20)$

$\implies 2x - 20 = 90 - 2y -20$

$\implies 2x + 2y = 90 - 20 + 20$

$\implies 2(x + y) = 90$

$\implies (x + y) = \frac{90}{2}$

$\implies (x + y) = 45\degree$

$\implies tan(x+y) = tan 45\degree$

$\implies tan(x+y) = 1$

Therefore.,

$\red {Value \: of \: tan(x+y) } \green {= 1}$

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