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

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

Grade:

2 Answers

manmeet singh chhina
18 Points
11 years ago

answer is 1

Jayesh Arun Kadam
34 Points
10 years ago

 

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


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