If `sin(x+20) = cos(x-10)` find the value of x.

a)90

b)60

c)45

d)40

e)30

### 1 Answer | Add Yours

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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