Question

Sin theta plus seven cos theta equal 5 then tan theta by 2

Answer 1

Answer:

tanθ/2= 1/2    and tanθ/2 = -1/3

Step-by-step explanation:

we know formula   sinθ= 2*tan(θ/2)/(1+tan²θ/2)    and

Cosθ = ( 1 - tan²(θ/2))/(1 + tan²(θ/2))

let’s assume that tanθ/2=p

put this value in given equation

2p/(1+p²) + 7(1-p²)/(1+p²) =5

2p + 7 - 7p² = 5 ( 1 + p²)

2p + 7 - 7p² = 5 + 5p²

12p² - 2p - 2 = 0

6p² - p - 1  = 0

6p² - 3p + 2p - 1 = 0

3p(2p - 1) + 1(2p - 1) = 0

(3p + 1)(2p-1) = 0

p = 1/2     and p = - 1/3

=> tanθ/2=1/2    and tanθ/2= -1/3