Question

In triangle ABC right angled at B, BC=7cm, AC-AB=1cm, then find the value of
(i) cosA+sinA (ii) tan C - cosecA+sinC.cosA (iii) tanA.secC

Answer 1

Answer:

option 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