2. If cost_ + cos-l-0 then prove CERT) 9x2

If sin x + sin y + sin z = 0 and cos x + cos y + cos z = 0 then prove that cot (x+y)/2 = cot z and cos (x-y)/2 = pm 1/2

If x in(0,pi/2) and cos x=1/3, then prove that sum_(n=0)^(oo)(cos nx)/(3^(n))=(3(3-cos x))/(10-6cos x+cos^(2)x)

Prove that cos 2 x cos ""x/2 - cos 3x cos ""(9x)/(2) = sin 5x sin ""(5x)/(2)

Prove that cos 2 x cos (x/2)-cos 3 x cos ((9x)/2)=sin 5 x sin ((5 x)/2)

Let l_(1) be the length of the latus rectum of the parabola 9x^(2)-6x+36y+19=0. Let l_(2), be the length of the latus rectum of the hyperbola 9x2-16y^(2)-18x-32y-151=0. Let n be the unit digit in the product of l_(1) and l_(2) The number of terms in the binomial expansion of (1+x)^(n) is

Prove that cos 2x cos "" x/2 -cos 3x cos " (9x)/(2) = sin 5x sin ""(5x)/(2).

Prove that cos 2x cos "" x/2 -cos 3x cos " (9x)/(2) = sin 5x sin ""(5x)/(2).

Prove that cos 2x cos "" x/2 -cos 3x cos " (9x)/(2) = sin 5x sin ""(5x)/(2).

Prove that cos 2x cos "" x/2 -cos 3x cos " (9x)/(2) = sin 5x sin ""(5x)/(2).