The sides of a triangle are `sin alpha, cos alpha, sqrt(1+sin alpha cos alpha)" for some " 0 lt alpha lt (pi)/(2)` then the greatest angle of the triangle is :

The sides of the triangle are sin alpha , cos alpha and sqrt(1+sinalphacosalpha) for some 0 lt alpha lt (pi)/2 . Then the greatest angle of the triangle is

If (sin alpha)^(x)+(cos alpha)^(x) ge 1,0 lt a lt (pi)/(2) then

If tan theta=(sin alpha- cos alpha)/(sin alpha+cos alpha) , then:

If Delta_(1) is the area of the triangle with vertices (0, 0), (a tan alpha, b cot alpha), (a sin alpha, b cos alpha), Delta_(2) is the area of the triangle with vertices (a sec^(2) alpha, b cos ec^(2) alpha), (a + a sin^(2)alpha, b + b cos^(2)alpha) and Delta_(3) is the area of the triangle with vertices (0,0), (a tan alpha, -b cot alpha), (a sin alpha, b cos alpha) . Show that there is no value of alpha for which Delta_(1), Delta_(2) and Delta_(3) are in GP.

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

If A=[[cosalpha, -sin alpha] , [sin alpha, cos alpha]] then A+A'=I then alpha=

The value of (sin(pi-alpha))/(sin alpha-cos alpha tan.(alpha)/(2))-cos alpha is

Which is equivalent to (sin^2 alpha + cos^2 alpha )/(cos alpha ) ?

If the angles alpha, beta, gamma of a triangle satisfy the relation, sin((alpha-beta)/(2)) + sin ((alpha -gamma)/(2)) + sin((3alpha)/(2)) = (3)/(2) , then The measure of the smallest angle of the triangle is

If the sides of a right angled triangle are {cos 2 alpha + cos 2 beta + 2 cos (alpha+beta)} and {sin 2 alpha+sin 2 beta + 2 sin (alpha+beta)} then the length of the hypotneuse is