if 2 cosx + sinx = 1 then what is the value of 7cosx + 6sinx

answer is 1

Cosx = (1-tan²x/2)/(1+tan²x/2)

Sin x = (2tanx/2)/(1+tan²x/2)

2cosx + sinx=1

2(((1-tan²x/2)/(1+tan²x/2)) + ((2tanx/2)/(1+tan²x/2))=1

Solving this we get quadratic in tanx/2

3tan²x/2 – 2tanx/2 -1=0

(3tanx/2+1)(tanx/2 -1)=0

Tanx/2 =1 or -1/3

7cosx + 6sinx

7((1-tan²x/2)/(1+tan²x/2)) + 6((2tanx/2)/(1+tan²x/2))

Putting value of Tanx/2, we get

When

Tanx/2 =1 Ans=6

When

Tanx/2=-1/3 Ans=2

Approved