Question

Prove that cos theta + cos((2pi)/3 + theta ) + cos((4pi)/3 + theta ) = 0

Answer 1

$\huge\mathtt\pink{♡Answer♡}$

a=cosx+cos(x+

3

2π

)+cos(x+

3

4π

)

a=cosx+2cos

⎝

⎜

⎜

⎛

2

x+

3

2π

+x+

3

4π

⎠

⎟

⎟

⎞

cos

⎝

⎜

⎜

⎛

2

x+

3

2π

−x−

3

4π

⎠

⎟

⎟

⎞

a=cosx+2cos

⎝

⎜

⎜

⎛

2

2x+

3

6π

⎠

⎟

⎟

⎞

cos

⎝

⎜

⎜

⎛

2

3

−2π

⎠

⎟

⎟

⎞

a=cosx+2cos(π+x)cos

3

π

a=cosx−2cosxcos

3

π

a=cosx−2cosx×

2

1

a=cosx−cosx=0

∴a=0

b=sinx+sin(x+

3

2π

)+sin(x+

3

4π

)

b=sinx+2sin

⎝

⎜

⎜

⎛

2

x+

3

2π

+x+

3

4π

⎠

⎟

⎟

⎞

cos

⎝

⎜

⎜

⎛

2

x+

3

2π

−x−

3

4π

⎠

⎟

⎟

⎞

b=sinx+2sin

⎝

⎜

⎜

⎛

2

2x+

3

6π

⎠

⎟

⎟

⎞

cos

⎝

⎜

⎜

⎛

2

3

−2π

⎠

⎟

⎟

⎞

b=sinx+2sin(π+x)cos

3

π

b=sinx−2sinxcos

3

π

b=sinx−2sinx×

2

1

b=sinx−sinx=0

∴b=0

Hence a+b=0 [Proved].

hope it helps ✅✅✅

plss make me as brainliest.

#MichAditi✨✌️

Answer 2

Answer:

please refer to the attached

please drop some ❤️❤️❤️

Step-by-step explanation:

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