Home
Class 12
MATHS
If a=cos 2alpha+i sin 2alpha, b =cos 2be...

If `a=cos 2alpha+i sin 2alpha, b =cos 2beta+i sin 2beta and c = cos 2gamma+i sin 2gamma`. Prove that.
(i) `sqrt(abc)+(1)/(sqrt(abc))=2cos(alpha+beta+gamma)`
(ii) `((a^(2)b^(2)+c^(2)))/(abc)=2cos2(alpha+beta-gamma)`

Promotional Banner

Topper's Solved these Questions

  • SAMPLE PAPER - 20 (UNSOLVED)

    FULL MARKS|Exercise PART - III (III. Answer any seven questions. Questions No. 40 is compulsory.)|10 Videos
  • SAMPLE PAPER - 2

    FULL MARKS|Exercise PART -IV (Answer the questions)|11 Videos
  • SAMPLE PAPER - 5

    FULL MARKS|Exercise PART -IV|13 Videos

Similar Questions

Explore conceptually related problems

If a = cos 2alpha + i sin 2 alpha, b = cos 2 beta + i sin 2 beta and c = cos 2gamma + i sin 2 gamma . Prove that . sqrt(abc) + 1/(sqrt(abc)) = 2 cos (alpha + beta + gamma)

If a = cos 2alpha + i sin 2 alpha, b = cos 2 beta + i sin 2 beta and c = cos 2gamma + i sin 2 gamma . Prove that . (a^2b^2 + c^2)/(abc) = 2 cos 2 (alpha + beta - gamma)

If a =cos alpha - i sin alpha, b= cos beta - i sin beta, c = cos gamma - i sin gamma , then ((a^2c^2 - b^2)/(abc)) is …………..

If x = cos alpha + i sin alpha , y = cos beta + i sin beta , prove that x^(m)y^(n)+1/(x^m y^n) = 2 cos (m alpha + n beta) .

If cos alpha + cos beta =0 = sin alpha + sin beta , then cos 2 alpha + cos 2 beta is equal to

IF cos ( alpha + beta ) =0 then sin ( alpha + 2 beta ) is equal to

If cos alpha + cos beta + cos gamma = sin alpha + sin beta + sin gamma = 0 , show that cos 3alpha + cos 3 beta + cos gamma = 3 cos (alpha + beta + gamma) and

If cos alpha + cos beta = 1//2 and sin alpha+ sin beta = 1//3 , then

If cos alpha + cos beta + cos gamma = sin alpha + sin beta + sin gamma = 0 , show that sin 3alpha + sin 3 beta + sin 3gamma = 3 sin (alpha + beta + gamma)

If cos (alpha - beta) + cos (beta - gamma) + cos (gamma - alpha) = (-3)/(2) then prove that cos alpha + cos beta+ cos gamma = sin alpha + sin beta + sin gamma = 0 .