If G, D and `theta` be the number of grades, degrees and radians in any angle, prove that : `D/90=G/100= (2 theta)/pi` .

If G, D and theta be the number of grades, degrees and radians in any angle, prove that : G=D+D/9 .

If G, D and theta be the number of grades, degrees and radians in any angle, prove that : G-D= (20 theta)/pi .

If theta - phi=pi/4 , prove that : (1 + tan theta)(1-tan phi)=2 .

Prove that the area of a sector of circle with radius r and central angle theta^@ is 1/2 r^2 theta .

The angles of a triangle are in A.P. and the number of degrees in the least to the number of radians in the greatest is as 60 : pi , find the angles in degrees and radians.

The base of a triangle is divided into three equal parts. If theta_(1), theta_(2), theta_(3) be the angles subtended by these parts at the vertex, then prove that (cot theta_(1) +cot theta_(2) ) (cot theta_(2)+ cot theta_(3))=4 cosec ^(2) theta _(2)

If the segments joining the points A(a , b)a n d\ B(c , d) subtends an angle theta at the origin, prove that : theta=(a c+b d)/((a^2+b^2)(c^2+d^2))

The number of solutions of cot(5pi sin theta )=tan (5 pi cos theta ), AA theta in (0,2pi) is

Prove that sin theta< theta< tan theta for theta in (0,pi/2) .