`1/(tan3alpha-tanalpha)-1/(cot3alpha-cotalpha)=cot2alpha`

Prove that: t a nalpha+2tan2alpha+4tan4alpha+8cot8alpha=cotalpha

Prove that: t a nalpha+2tan2alpha+4tan4alpha+8cot8alpha=cotalpha

If cot^3alpha+cot^2alpha+cotalpha=1 then (a) cos2alpha.tanalpha=-1 (b) cos2alpha.tanalpha=1 (c) cos2alpha-tan2alpha=1 (d) cos2alpha-tan2alpha=-1

prove that : tan(alpha)+2 tan(2alpha) +4(tan4alpha)+8cot(8alpha) = cot(alpha)

If (tanalpha+tanbeta)/(cot alpha+cot beta)+{cos(alpha-beta)+1}^(-1)=1, then tan alpha tan beta is equal to

If (3pi)/4 lt alpha lt pi , then sqrt(2cotalpha+1/(sin^2alpha)) is equal to (a) 1-cotalpha (b) 1+cotalpha (c) -1+cotalpha (d) -1-cotalpha

If 3π/4<α<π, then sqrt(2cotalpha+1/(sin^2alpha)) is equal to (a) 1+cotalpha (b) -1-cotalpha (c) 1-cotalpha (d) -1+cotalpha

If u=cot^(-1)sqrt(tanalpha)-tan^(-1)sqrt(tanalpha),t h e n tan(pi/4- u/2) is (a) sqrt(tanalpha) (b) sqrt(cotalpha) (c) tanalpha (d) cot alpha

Which of the following identities, wherever defined, hold(s) good? (a)cotalpha-tanalpha=2cot2alpha (b)tan(45^0+alpha)-tan(45^0-alpha)=2cos e c2alpha (c)tan(45^0+alpha)+tan(45^0-alpha)=2sec2alpha (d)tanalpha+cotalpha=2tan2alpha

Prove that cot alpha - tan alpha =2 cot 2 alpha.