1.

if theta =30° verify the following :- (a) cos 3 theta° = 4 cos ^3 theta - 3 cos theta (B) sin 3 theta° = 3 sin theta - 4 sin ^3 theta PROPER ANSWER=BRAINLIEST

Answer»

Solution :-

I m assume theta = x = 30°

(a) cos3x = 4cos³x - 3cosx

PUTTING x = 30° both SIDES we get,

→ COS(3*30°) = 4cos³30° - 3cosx

→ cos90° = 4cos³30° - 3cosx

values :-

  • cos90° = 0
  • cos30° = (√3/2)

Putting values both sides Now,

→ 0 = 4(√3/2)³ - 3(√3/2)

→ 0 = 4(3√3/8) - (3√3/2)

→ 0 = (12√3/8) - (3√3/2)

→ 0 = (3√3/2) - (3√3/2)

→ 0 = 0 (Verified) .

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(B) sin3x = 3sinx - 4sin³x

Putting x = 30° both sides we get,

→ sin(3*30°) = 3sinx - 4sin³30°

→ sin90° = 3sin30° - 4sin³30°

values :-

  • sin90° = 1
  • sin30° = (1/2)

Putting values both sides Now,

→ 1 = 3(1/2) - 4(1/2)³

→ 1 = (3/2) - 4(1/8)

→ 1 = (3/2) - (1/2)

→ 1 = (3 - 1)/2

→ 1 = (2/2)

→ 1 = 1 (Verified.)

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