Question

If $tan A=\frac{5}{12}$, find the value of (sin A + cos A) sec A.

Answer 1

SOLUTION :  

Given : tan A = 5/12.

We have to find the value of (sin A + cos A ) sec A .

In right angle ∆ ,  

tan A =  perpendicular/base = 5/12.

perpendicular = 5 , base = 12

Hypotenuse = √( perpendicular)² + (Base)²

[By Pythagoras theorem]

Hypotenuse = √ 5² + 12² = √25 + 144 = √169

Hypotenuse = 13  

sin A  = perpendicular/hypotenuse = 5/13

cos A = base/ hypotenuse = 12/13

sec A = hypotenuse / base = 13/12

The value of (sin A + cos A ) sec A :  

= (5/13 + 12/13) × 13/12

=[ (5 + 12)/13] × 13/12

= (17/13) × (13/12)

(sin A + cos A ) sec A = 17/12

Hence, the value of (sin A + cos A ) sec A is 17/12 .

HOPE THIS ANSWER WILL HELP YOU…

Answer 2

hey mate here is your answer ✌♥✌

given.....

tan A=5/12

to find.....

(sinA+cosA) sec A

=sinA . secA+cosA . secA

=sinA / cosA+cosA / cosA........(1 / cosA = secA)

=tanA+1...........(sinA/cosA=tanA)

=5/12 +1

=5+12/12

=17/12

hope it will help you

mark me brainliest ✌