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Prove that:
Please solve this question.

 see attachment

Step-by-step explanation:

Given: cos 330 = √3/2

Prove that tan (165) = √3 - 2

Step-by-step explanation:

cos330° = cos(360° - 30°) = cos(2π - 30°)

Using, cos(2π - x) = cosx, x < 90°

=> cos(2π - 30°)

=> cos(30°)

=> √3/2 , proved

(ii): tan(165°) = tan(180° - 15°) = tan(π - 15°)

Using, tan(π - x) = - tanx

=> tan(π - 15°)

=> - tan15°

=> - (-√3 + 2)

=> √3 - 2 proved

For tan15° :

Using, tan2x = 2tanx/(1 - tan²x)

tan30° = 2tan15°/(1 - tan²15°)

1/√3 = 2tan15° / (1 - tan²15°)

1 - a² = 2√3 a {a = tan15°}

Solving this we get, a = -√3±2

As a = tan15°, it can't be -ve, thus

a = tan15° = -√3 + 2

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step-by-step explanation: