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)`

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 . prove that (T_(3)-T_5)/(T_1)=(T_5-T_7)/(T_3) .

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

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

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

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 ,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)x+cos^(n)x, prove that 2T_(6)-3T_(4)+1=0