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

Prove the following identity: (1+cottheta-cos e ctheta)(1+t a ntheta+s e ctheta)=2

Prove the following identity: (cosectheta-sintheta)(s e ctheta-costheta)(t a ntheta+cottheta)=1

Prove the following identity: costheta(t a ntheta+2)(2t a ntheta+1)=2s e ctheta+5sintheta

Prove that: (sin2theta)/(1+cos2theta)=t a ntheta

Prove that: (sin2theta)/(1+cos2theta)=t a ntheta

Solve the following equation: t a ntheta+t a n2theta+t a n3theta=0