If the sides of a right triangle are in A.P., then the sum of the sines of the two acute angles is:
Explanation for the correct option:
Step 1: Find the sides of the triangle
It is given that the sides of the right-angled triangle are in A.P.
So, let the sides be
The hypotenuse is the longest side of a triangle
So, Hypotenuse and other sides are and
Applying Pythagoras theorem, , we get,
Either or
So,
Replace this in , we get,
Step 2: Evaluate the trigonometric value of the acute angles
We need to evaluate the of the acute angles,
So, as
When is the base,
When is the base,
Therefore, the sine of the acute angles are
The sum of the sine of two acute angles
Thus, option (A) is the correct option.