Question

In the given figure below, triangle ABC is right angled at B , BC = 7 cm and AC- AB=1cm. Find the

value of cosA+SinA​

Answer 1

Answer:

Given: ΔABC has a right angle at B, BC = 7 cm, AC – AB = 1 cm.

We need to find the value of cos A – sin A.

AC – AB = 1 ........ (1)

Applying Pythagoras' theorem in ΔABC, we get

AC² = AB² + BC² (since AC is opposite the right angle, angle B, it is the hypotenuse)

AC² – AB² = 7²

(AC – AB)(AC + AB) = 49

Using Equation (1), we get

AC + AB = 49 ......... (2)

After adding Equations (1) and (2), we get

Substituting the obtained value above into Equation (2), we get

Using the definitions of sin A and cos A, we get

Therefore, given the provided information, cos A – sin A = 17/25.