Question

If $A$ is an acute angle in a right $△ABC$, 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

Answer 1

Answer: (B)

greater than one

$△ABC$ is a right angled triangle and right angle at $B$

$\sin A=\frac{BC}{AC},$ $\cos A=\frac{AB}{AC}$
$⟹\sin A+\cos A=\frac{BC}{AC}+\frac{AB}{AC}$
$=\frac{BC+AB}{AC}$
[We know that sum of two sides of a triangle is greater than the third side]
$⟹\sin A+\cos A>\frac{AC}{AC}=1$

Hence, $\sin A+\cos A>1$