Question

Write 'True' or 'False' and justify your answer in the following: 

The value of sin θ + cos θ is always greater than 1.

Answer 1

This statement is false.

Explanation:

Consider the table.

θ	0°	30°	45°	60°	90°
`sin θ`	`0`	`1/2`	`1/sqrt2`	`sqrt3/2`	`1`
`cosθ`	`1`	`sqrt3/2`	`1/sqrt2`	`1/2`	`0`

Here, 

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

Therefore, the given statement is false.