If `T_n=sin^n x+cos^(pi)x` prove that `(T_3-T_5)/T_1=(T_5-T_7)/T_3`

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^(n)theta+cos^(n)theta, prove that (T_(3)-T_(5))/(T_(1))=(T_(5)-T_(7))/(T_(3))

If T_n = sin^(n)theta + cos^(n)theta then prove that (T_5 -T_3): (T_7- T_5) = T_1 :T_3 .

If T_(n)=sin^(n)theta+cos^(n)theta ,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)-15T_(8)+10T_(6)-1=0

If T_(n)=sin^(n)theta+cos^(n)theta then (T_(3)-T_(5))/(T_(1))=?

Let T_(k)=sin^(k)x+cos^(k)x For all x if T_(1)T_(5)+T_(3)T_(5)=T_(1)T_(7)+T_(3)T_(n) then n=

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

If t_0,t_1, t_2,...,t_n are the terms in the expansion of (x+a)^n then prove that (t_0-t_2+t_4-...)^2+(t_1-t_3+t_5-...)^2=(x^2+a^2)^n .

If x=cos t and y=sin t, prove that (dy)/(dx)=(1)/(sqrt(3)) at t=(2 pi)/(3)