Multiple angle formulae Questions

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?

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 minimum value of p?

Direction for Questions (41-43):

Consider the following for the three (03) items that follow

: Let p = sin 35°, q = sin 25° and r = sin(–95°).

What is (p² + q² + r²) equal to?

Direction for Questions (41-43):

Consider the following for the three (03) items that follow: Let p = sin 35°, q = sin 25° and r = sin(–95°).

 What is (pq +qr + rp) equal to?

Direction for Questions (41-43):

 Consider the following for the three (03) items that follow: Let p = sin 35°, q = sin 25° and r = sin(–95°).

What is (p + q + r) equal to?

If tan^–1 k + tan^-1 1/2 =π/4