Multiple angle formulae

How many values of θ, where -π < θ < π, satisfy both the equations cotθ = −3 and cosecθ = –2 simultaneously?

Direction for Questions (46-48): Consider the following for the three (03) items that follow: The sides of a triangle ABC are AB = 3 cm, BC = 5 cm and CA = 7 cm.

 What is the area of the area of the triangle?

Direction for Questions (46-48): Consider the following for the three (03) items that follow: The sides of a triangle ABC are AB = 3 cm, BC = 5 cm and CA = 7 cm.

What is Angle B equal to?

Direction for Questions (46-48): Consider the following for the three (03) items that follow: The sides of a triangle ABC are AB = 3 cm, BC = 5 cm and CA = 7 cm.

 Consider the following statements:

I. The triangle is an obtuse-angled triangle.

II. The sum of acute angles of the triangle is also acute.

Which of the statements given above is/are correct?

Direction for Questions (44-45): Consider the following for the two (02) items that follow:

 Let p = [sin a – sin(a – 90°)].

What is the maximum value of p?