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

a. 0

b. 1

c. 1/2

d. √3/2

**Solution:**

Given, the triangle ABC is a right triangle with C at right angle.

We have to find the value of cos(A+B)

We know that the sum of all the three interior angles of a triangle is always equal to 180°

So, ∠A + ∠B + ∠C = 180°

∠A + ∠B + 90° = 180°

∠A + ∠B = 180° - 90°

∠A + ∠B = 90°

So, cos (A+B) = cos 90°

Using the trigonometric ratios of angles,

cos 90° = 0

Therefore, the value of cos(A + B) is zero.

**✦ Try This: **If ∆DEF is right angled at E, then the value of sin (D + F) is

Given, the triangle DEF is a right triangle with E at right angles.

We have to find the value of sin(D + F)

We know that the sum of all the three interior angles of a triangle is always equal to 180°

So, ∠D + ∠E + ∠F = 180°

∠D + ∠F + 90° = 180°

∠D + ∠F = 180° - 90°

∠D + ∠F = 90°

So, sin (D + F) = sin 90°

Using the trigonometric ratio of angels,

sin 90° = 1

Therefore, the value of sin(D + F) is 1.

**☛ Also Check: **NCERT Solutions for Class 10 Maths Chapter 8

**NCERT Exemplar Class 10 Maths Exercise 8.1 Problem 8**

## If ∆ABC is right angled at C, then the value of cos (A+B) is a. 0, b. 1, c. 1/2, d. √3/2

**Summary:**

If ∆ABC is right angled at C, then the value of cos (A+B) is 0

**☛ Related Questions:**

- If sinA + sin2 A = 1, then the value of the expression (cos2 A + cos4 A) is a. 1, b. 1/2, c. 2, d. 3
- Given that sinα = 1/2 and cosβ = 1/2, then the value of (α + β) is a. 0°, b. 30°, c. 60°, d. 90°
- The value of the expression [(sin222°+sin268°)/(cos222°+cos268°)] +sin263° +cos 63°sin 27°. a. 3, b. . . . .

visual curriculum