If `sin(x+20) = cos(x-10)`  find the value of x. a)90 b)60 c)45 d)40 e)30

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jeew-m | College Teacher | (Level 1) Educator Emeritus

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we know the following rule from trigonometry.

`sin(90-theta) = costheta`

 

`x+20 = 90-(70-x)`

 

`sin(x+20) = sin(90-(70-x)) = cos(70-x)`

 

`sin(x+20) = cos(x-10)`

`cos(70-x) = cos(x-10)`

Since all the answers are less than of equal to 90 we can say;

`70-x = x-10`

`x = 40`

 

So the answer is x = 40. Correct answer is d)

 

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