Question

10. In Δ ABC , L B= 90 ⁰ if BC = 7 cm and AC — BC = 1 cm find the value of

cos A + sin A ?​

Answer 1

Step-by-step explanation:

ΔABC is right angled at B, so AC is the hypotenuse.

AC−AB=1 ...Given ....(1)

By Pythagoras theorem,

AC 2 =AB 2+BC 2

BC 2 =AC 2 −AB 2

7 ^2 =(AC−AB)(AC+AB)

49=1(AC+AB)

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

Adding (1) and (2) we get,

⇒2AC=50

⇒AC=25 cm

Sbstitute in eq (2), we get

AB=24 cm.

Now, cosA+sinA=

AC/AB + AC/BC = 25/24 + 25/7 = 25/31

⇒cosA+sinA=

25/31