Question

in triangle abc right angle at b if tan a =1/root 3 find value of (1) sina cosc +cosa sinc (2) cosa cosc - sina sinc​

Answer 1

Answer:

Step-by-step explanation:

tanA=1/√3

tanA= tan 30°

Comparing LHS and RHS,we get : A=30°

1) we know that  

sum of all sides are 180

than

∠a + ∠b + ∠c = 180

30 + 90 + ∠c = 180

∠c = 180-120

∠c = 60

I hope you can solve it now.

Answer 2

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

now I give u all the values ..

now u have to put the values and your ans is come with in your hand

I hope I will help u

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