Question

sin(x+4π/9)=a, then cos(x+7π/9)=?​

Answer 1

Answer:

sin^2(π/18)+sin^2(π/9)+sin^2(7π/18)+sin^2(4π/9)=2

L.H.S.

we know that , cos2A=1–2.sin^2(A). or sin^2(A)=1/2.(1-cos2A).

=1/2.[1-cos(π/9)]+1/2.[1-cos(2π/9)]+1/2.[1-cos(7π/9)]+1/2.[1–cos(8π/9)].

=1/2.[4-cos(π/9)-cos(2π/9)-cos(7π/9)-cos(8π/9)].

=1/2.[4-cos(π-8π/9)-cos(π-7π/9)-cos(7π/9)-cos(8π/9)].

=1/2.[4+cos(8π/9)+cos(7π/9)-cos(7π/9)-cos(8π/9)].

=1/2.[4+0]

=1/2×(4).

=2. Proved.

OR

LHS=Sin2π/18+sin2π/9+sin27π/18+sin24π/9LHS=Sin2π/18+sin2π/9+sin27π/18+sin24π/9

=sin210°+sin220°+sin270°+sin280°=sin210°+sin220°+sin270°+sin280°

=Sin210°+sin280°+sin220°+sin280°=Sin210°+sin280°+sin220°+sin280°

=Sin210°+sin2(90°−10°)+sin220°+sin2(90°−20°)=Sin210°+sin2(90°−10°)+sin220°+sin2(90°−20°)

=(Sin210°+cos210°)+(sin220°+cos220°)

=1+1=2=RHS

I hope this both R help u

Answer 2

The value of cos(x+7π/9) is equal to ((√(1-a²) - a)√3)/2.

Step-by-step explanation:

According to the given information, the value of sin(x+4π/9) is equal to a.

We need to find the value of cos(x+7π/9).

Now, the angle 4π/9 is actually (4*180)/9 = 80°

Then, by the problem, we get,

sin(x+80) = a

Now, we know the well know trigonometrical identity that is,

sin²x + cos²x = 1.

Now, this can also be written as,

cos x = √(1-sin²x)

Now, applying this formula, we get,

cos (x+80) = √(1-a²)

Now, we need to find the value of cos(x+7π/9)

Now, the angle 7π/9 can be written as (7*180)/9 that is, 140°.

Now, cos (x+140)

=cos ( x + 80 + 60)

Now, we know that, the formula of cos (a+b) = cos a* cos b - sin a* sin b

Then, using this formula, we get,

cos(x+80)cos(60) - sin(x+80) sin(60)

Now, the value of cos 60 is equal to 1/2 and the value of sin 60 is equal to √3/2.

Now, putting the known values in the above relation, we get,

cos(x+80)cos(60) - sin(x+80) sin(60)

=√(1-a²)*(1/2) - a*(√3/2)

=((√(1-a²) - a)√3)/2

Thus, the value of cos(x+7π/9) is equal to ((√(1-a²) - a)√3)/2.

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