# The value of sinθ + cosθ is always greater than 1. Write ‘True’ or ‘False’ and justify your answer

**Solution:**

Given, the statement is “the value of sinθ + cosθ is always greater than 1”

We have to determine if the given statement is true or false.

θ |
0° |
30° |
45° |
60° |
90° |

sinθ |
0 |
1/2 |
1/√2 |
√3/2 |
1 |

cosθ |
1 |
√3/2 |
1/√2 |
1/2 |
0 |

By using trigonometric ratio of angles,

Sin 0° + cos 90° = 0 + 0 = 0

sin 90° + cos 90° = 1 + 0 = 1 which is not greater than one.

Therefore, the value of sinθ + cosθ is always greater than 1 is false.

**✦ Try This: **If tan A = a/b then (cos A - sin A)/(cos A + sin A) = ?

Given, tan A = a/b

We have to find (cos A - sin A)/(cos A + sin A)

Dividing numerator and denominator by cos A,

= (1 - sin A/cos A)/(1 + sin A/cos A)

= (1 - tan A)/(1 + tan A)

= (1 - a/b)/(1 + a/b)

= (b - a)/b / (b + a)/b

= (b - a)/(b + a)

Therefore, (cos A - sin A)/(cos A + sin A)= (b - a)/(b + a)

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

**NCERT Exemplar Class 10 Maths Exercise 8.2 Sample Problem 1**

## The value of sinθ + cosθ is always greater than 1. Write ‘True’ or ‘False’ and justify your answer

**Summary:**

The sine of an angle is the ratio of the opposite side and the hypotenuse and the cosine of an angle is the ratio of the adjacent side and the hypotenuse. The statement “The value of sinθ + cosθ is always greater than 1” is false

**☛ Related Questions:**

- The value of tanθ (θ < 90°) increases as θ increases. Write ‘True’ or ‘False’ and justify your answe . . . .
- tanθ increases faster than sinθ as θ increases. Write ‘True’ or ‘False’ and justify your answer
- The value of sinθ is a+(1/a), where ‘a’ is a positive number. Write ‘True’ or ‘False’ and justify y . . . .

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