If `pi/2 lt alpha lt pi` then the distance between two points `(tan alpha,2)` and `(0,1)` is

If (pi)/(2)

If 0 lt alpha lt pi/6 , then the value of (alpha cosec alpha ) is

If (3pi)/(2) lt alpha lt 2 pi , find the modulus and argument of (1 - cos 2 alpha) + i sin 2 alpha .

If 0 lt alpha lt pi/2 then show that tanalpha+cotgtsinalpha+cosalpha

If 0 lt alpha lt (pi)/(2) and the eccentricity of the ellipse x^(2) tan^(2) alpha + y^(2) sec^(2) alpha = 1 is 1//2 , then alpha

If 0 lt alpha lt (pi)/(3) , then prove that alpha (sec alpha) lt (2pi)/(3).

If (pi)/(2)lt alpha lt (3pi)/(4) , then sqrt(2tan alpha+(1)/(cos^(2)alpha)) is equal to

If 13 sin alpha = 12, where pi//2 lt alpha lt pi, and 3 sec beta = 5, where 3pi//2 lt beta lt 2pi , evaluate : 5tan alpha+3 tan^(2)beta.