question_answer

If A is an acute angle of a \[\Delta ABC,\]right angled at B, then the value of \[\sin A+\cos A\] is:

A) equal to one

B) greater than one

C) less than one

D) equal to two

Correct Answer: B

Solution :

[b] We have,\[\sin A+\cos A\]

\[=\frac{BC}{AC}+\frac{AB}{AC}=\frac{BC+AB}{AC}>\frac{AC}{AC}>1\]

[The sum of the length of any two sides of a triangle is always greater than the length of the remaining third side.]