`1+tan alpha*tan((alpha)/(2))`

[[1,-tan((alpha)/(2))tan((alpha)/(2)),1]][[1,-tan((alpha)/(2))tan((alpha)/(2)),1]]

[ 7.If 0ltalphaltbetalt(pi)/(2) then [ 1) (tan beta)/(tan alpha)lt(alpha)/(beta), 2) (tan beta)/(tan alpha)gt(alpha)/(beta) 3) (tan alpha)/(tan beta)lt(alpha)/(beta) , 4) none ]]

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 .

Prove that tan alpha+2 tan 2 alpha+2^(2)tan^(2)alpha+..............+2^(n-1)tan2^(n-1)alpha+2^(@)cot2^(@)alpha=cotalpha

(1)/(tan3 alpha-tan alpha)-(1)/(cot3 alpha-cot alpha)=cot2 alpha

if (1+tan alpha)(1+tan4 alpha)=2 where alpha in(0,(pi)/(16)) then alpha equal to

If 0 lt alpha lt (pi)/(16) and (1+tan alpha)(1+tan4alpha)=2 , then the value of alpha is equal to

If sec alpha=(5)/(4), verify that (tan alpha)/(1+tan^(2)alpha)=(sin alpha)/(sec alpha)

If (1+tan alpha)(1+tan4 alpha)=2,alpha in(0,(pi)/(16)) then alpha is equal to (a) (pi)/(20) (b) (pi)/(30) (c) (pi)/(40) (d) (pi)/(60)