Test Preparation on Mathematics-Trigonometry

In triangle PQR, ∠ R =2π. If tan (P/2)and tan (Q/2 )are the roots of the equationa x2+ b x + c = 0, a ≠ 0, then

In triangle ABC, let ∠ C =π/2. If r is the inradius and R is the circumradius of thetriangle ABC, then 2 ( r + R ) equals

If cos- 1x - cos- 1y/2= α, then 4x2- 4xy cos α + y2 is equal to

Let α, β be such that π < α - β < 3π. If sin α + sin β = - 21/65, then the value ofcos α - β/2 is

If =

then difference betweenthe maximum and minimum values of u2 is given by

The sides of a triangle are sin α, cos α and √1 + sin α cos α for some 0 < α <2π.Then the greatest angle of the triangle is

A person standing on the bank of a river observes that the angle of elevation of thetop of a tree on the opposite bank of a river is 60° and when he retires 40 m awayfrom the tree, the angle of elevation becomes 30°. The breadth of the river is