Question

In triangle ABC, right-angled at B, if tan A =1÷ route13.find the value of

1: sinA cosC + cosA sinC
2: cosA cosC + sinA sinC​

Answer 1

We have a right angled ∆ABC in which angle B= 90° .

tan A = 1/√3

now.

tanA = 1/√3=BC/AB

let,

BC=k and AB =√3k

by (PGT)

AC^2= AB^2 +BC^2

AC^2= (√3K)^2 + (K)^2 = 3K^2+K^2

AC^2= 4K^2

NOW,,,

sinA = perpendicular/hypotenuse

k/2k =1/2 ,

cosA = base/hypotenuse

√3k/2k = √3/2

sin C = perpendicular / hypotenuse

= √3k /2k = √3/2

cos C = base / hypotenuse = k /2k =1/2

Answer 2

Answer:

Step-by-step explanation

Given:

tanA=1/√3

A=30°

since B is right angle, C=60°

Now,

sinA.cosC + cosA.sinC

=sin(A+C)

=sin(30°+60°)

=sin90°

=1

cosA.cosC - sinA.sinC

=cos(A+C)

=cos(30°+60°)

=cos90°

=0

                                      I HOPE IT IS HELPFUL