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°.
