`cot^2 alpha=1+a^2` then `cosec alpha+cot^3 alpha sec alpha=`

cot^(2)alpha=1+a^(2) then cos ec alpha+cot^(3)alpha sec alpha=

Prove that: (tan^(3)alpha)/(1+tan^(2)alpha)+(cot^(3)alpha)/(1+cot^(2)alpha)=sec alpha cosec alpha-2sin alpha cos alpha

Show that 1 + cot^2 alpha / (1+ cosec alpha) = cosec alpha

Prove that : [1+ cot alpha- sec (pi/2+alpha)] [1+ cot alpha+ sec (pi/2+alpha)]= 2 cot alpha .

If 4n alpha=pi then cot alpha cot2 alpha cot3 alpha...cot(2n-1)alpha n in Z is equal to

"If "0ltalphaltpi/2 " and " sin alpha + cos alpha + tan alpha + cot alpha + sec alpha + cosec alpha = 7 " then " "show that " sin 2 alpha " is a root of " x^(2) - 44x - 36 = 0

P=[[sec alpha,tan alpha-cot alpha,cos alpha]] and Q=[[-cos alpha,tan alpha-cot alpha,-sec alpha]]

If (3pi)/4 < alpha < pi , then sqrt(cosec^2 alpha+2 cot alpha) is equal to