NCERT Exemplar Solutions
Class 10 - Mathematics - CHAPTER 8: Introduction to Trignometry and Its Applications - Exercise 8.1
Question 10

Question. 10

Given \(\sin\alpha=\dfrac{1}{2}\) and \(\cos\beta=\dfrac{1}{2}\), the value of \(\alpha+\beta\) is

(A)

\(0^\circ\)

(B)

\(30^\circ\)

(C)

\(60^\circ\)

(D)

\(90^\circ\)

Step 1: We are told that \(\sin\alpha = \tfrac{1}{2}\).

From standard trigonometric values, \(\sin 30^\circ = \tfrac{1}{2}\).

So, \(\alpha = 30^\circ\) (taking the acute angle).

Step 2: We are also told that \(\cos\beta = \tfrac{1}{2}\).

From standard values, \(\cos 60^\circ = \tfrac{1}{2}\).

So, \(\beta = 60^\circ\) (taking the acute angle).

Step 3: Now we add the two angles.

\(\alpha + \beta = 30^\circ + 60^\circ = 90^\circ\).

Final Answer: \(90^\circ\).