Question

if x is acute and sin(x+10∘ )=cos(3x−68∘ ), find x in degrees.

Answer 1

$Given \: Sin ( x + 10 ) = Cos ( 3x - 68 )$

$\implies Sin ( x + 10 ) = Sin [ 90 - ( 3x - 68 )]$

$\implies x + 10 = 90 - ( 3x - 68 )$

$\implies x + 10 = 90 - 3x + 68$

$\implies x + 3x = 90 + 68 -10$

$\implies 4x = 158 - 10$

$\implies 4x = 148$

$\implies x = \frac{148}{4}$

$\implies x = 37$

Therefore.,

$\red{ Value \: of \: x } \green { = 37 }$

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Answer 2

Answer:

GivenSin(x+10)=Cos(3x−68)

⟹Sin(x+10)=Sin[90−(3x−68)]

⟹x+10=90−(3x−68)

⟹x+10=90−3x+68

⟹x+3x=90+68−10

⟹4x=158−10

⟹4x=148

⟹x= 148/4

⟹x=37

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