If `T_n=sin^n x+cos^n x`, prove that `2T_6-3T_4+1=0`

Prove the trigonometric identities: If T_n=sin^ntheta+cos^ntheta, prove that (T_3-T_5)/(T_1)=(T_5-T_7)/(T_3)

If T_n=sin^ntheta+cos^ntheta , prove that (i) (T_3-T_5)/(T_1)=(T_5-T_7)/(T_3) (ii) 2T_6-3T_4+1=0 (iii) 6T_(10)-15 T_8+10 T_6-1=0

If T_n =sin^n theta+cos^n theta, then (T_6-T_4)/T_6 =m holds for values of m satisfying (A) m in [-1, 1/3] (B) m in [0, 1/3] (C) m in [-1,0] (D) m in [-1, - 1/2]

If T_(n)=cos^(n)theta+sin ^(n)theta, then 2T_(6)-3T_(4)+1=

If (1+x)^n=c_0+C_1x+C_2x^2++C_n x^n , using derivtives prove t h a t C_1-2C_2+3C_3++(-1)^(n-1)nC_n=0

In an A.P., prove that : T_(m+n) + T_(m-n) = 2*T_(m)

If 3t a n At a n B=1, prove that 2cos(A+B)=cos(A-B)dot

(i) If f(x) = int_(0)^(sin^(2)x)sin^(-1)sqrt(t)dt+int_(0)^(cos^(2)x)cos^(-1)sqrt(t) dt, then prove that f'(x) = 0 AA x in R . (ii) Find the value of x for which function f(x) = int_(-1)^(x) t(e^(t)-1)(t-1)(t-2)^(3)(t-3)^(5)dt has a local minimum.

If costheta=cosalphacosbeta , prove that t a n(theta+alpha)/2t a n(theta-alpha)/2=t a n^2beta/2 .

If (costheta=cosalphacosbeta , prove that t a n(theta+alpha)/2t a n(theta-alpha)/2=t a n^2beta/2 .