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

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

Show that sqrt((1+cos alpha)/(1-cos alpha))=cosec alpha + cot alpha

Prove that : 1+(cot^(2)alpha)/(1+"cosec"alpha)="cesec"alpha

If sqrt((1+cos alpha)/(1-cos alpha))=cosec alpha + cot alpha , then the quadrants in which alpha lies are

"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

show that (1-sin^2 alpha)(1-cos^2 alpha)(1+cot^2 alpha)(1+tan^2 alpha) = 1.

show that 1 + (cot^2 theta/ (1 + cosec theta)) = cosec theta

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

(sin alpha)/(1+cos alpha)+(1+cos alpha)/(sin alpha)=2cosec alpha

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