If`2t a n^2alphat a n^2betat a n^2gamma+2t a n^2alphat a n^2beta+t a n^2betat a n^2gamma+t a n^2gammat a n^2alpha=1,` prove that `s in^2alpha+s in^2beta+s in^2gamma=1` .

If tan^(2)alpha tan^(2)beta+tan^(2)beta tan^(2)gamma+tan^(2)gamma tan^(2)alpha+2tan^(2)alpha tan^(2)beta tan^(2)gamma= 1 .(where alpha,beta,gamma in R-{(n pi)/(2)},n in I ) Value of cos2alpha+cos2 beta+cos2gamma is equal to -

If n tan alpha=(n+1)tan beta then show that tan(alpha-beta)=(sin2 beta)/(2n+1-cos2 beta)

If tan(alpha+beta)=n tan(alpha-beta) then show that (n+1)sin2 beta=(n-1)sin2 alpha

Prove that : tan^(-1){(cos2\ alphasec2\ beta+cos2betasec2alpha)/2}=tan^(-1){t a n^2(alpha+beta)t a n^2(alpha-beta)}+tan^(-1)1

If "tan" alpha= n tan beta and sin alpha =m sin beta prove that : cos^(2)alpha=(m^(2)-1)/(n^(2)-1)

Prove that: tan alpha +2tan 2alpha+ 2^(2)tan 2^(2)alpha +..... + 2^(n-1) tan 2^(n-1)alpha + 2^n cot 2^n alpha=cotalpha .

if tan beta=(n sin alpha cos beta)/(1-n sin^(2)alpha) then prove that tan(alpha-beta)=(1-n)tan alpha

if tan beta=(n sin alpha cos beta)/(1-n sin^(2)alpha) then prove that tan(alpha-beta)=(1-n)tan alpha

(a) The displacement s of a particale in time t related as s = alpha + beta t + gamma t^(2) + delta t^(2) (b) The veloctiy v of particle varies with time as v = alpha t + beta t^(2) + (gamma )/(t + s) Findk the dimension fo alpha, beta, gamma and delta .

alpha and beta are the roots of x^2-x-1=0 and S_n=2023 alpha^n 2024 beta^n then