This is the basic and conceptual question from trigonometry, topic – trigonometric identities in which we have given that sinθ=cos(θ-45°) and here θ is an acute angle, we have to find the value of θ.
RS Aggarwal, Class 10, chapter 13C, question no 31
We know that,
sinθ=cos(90−θ)
∴sinθ=cos(θ−45∘)
cos(90∘−θ)=cos(θ−45∘)
(90∘−θ)=(θ−45∘)
2θ=90∘+45∘=135∘
θ=135∘/2
θ=62 1/2∘