Question

if cos theta: sin theta =1:2,then find the value of 8 cos theta -2sin theta /4 cos theta+3 sin theta​

Answer 1

Answer:

2/5

Step-by-step explanation:

given data

cos theta:sin theta=1:2

cos theta/sin theta=1/2

cos theta by sin theta is nothing but cot theta

so

cot theta=1/2

by using right angled triangle

cot theta = adjacent side of angle theta/ opposite side of angle theta

see the above given diagram

hypotenuse = root 5

then

sin theta = 2/root 5

2sin theta= 2(2/root5)=4/root5

3sin theta= 3(2/root5)= 6/root5

cos theta=1/root5

8cos theta=8(1/root5)=8/root5

4 cos theta= 4(1/root5)=4/root5

now the required answer is

8 cos theta - 2sin theta/ 4 cos theta+3 sin theta

=8/root5-4/root5 / 4/root5+ 6/root5

= 8-4/root5 / 4+6/root5

=4/10

=2/5

i think it will help you all the best