Can someone help me on this?

Step-by-step explanation: We are given to find the value of x from the following trigonometric equation:

sin55=cosx

We know that the sine of any acute angle is equal to the cosine of its complement and cosine of any acute angle is equal to the sine of its complement.So, from equation (i), we get

sin55 ∘ =cosx

⇒sin55 ∘ =sin(90 ∘−x)

⇒55 ∘ =90 ∘ −x

⇒x=90 ∘ −55 ∘

⇒x=35 ∘

Thus, the required value of x is 35°.