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

Question. 8

If \(\triangle ABC\) is right angled at \(C\), then the value of \(\cos(A+B)\) is

(A)

(B)

(C)

\(\dfrac{1}{2}\)

(D)

\(\dfrac{\sqrt{3}}{2}\)

Step 1: In any triangle, the sum of the three angles is always \(180^\circ\).

So, \(A + B + C = 180^\circ\).

Step 2: The question says that the triangle is right-angled at \(C\). That means \(C = 90^\circ\).

Step 3: Substitute \(C = 90^\circ\) in the equation:

\(A + B + 90^\circ = 180^\circ\)

Step 4: Subtract \(90^\circ\) from both sides:

\(A + B = 90^\circ\)

Step 5: Now, we need to find \(\cos(A+B)\).

Since \(A+B = 90^\circ\), we get:

\(\cos(90^\circ) = 0\).

Final Answer: \(\cos(A+B) = 0\).