A Recall of Basic Results

If x = `sum_("n" = 0)^oo cos^(2"n") theta, y = sum_("n" = 0)^oo sin^(2"n") theta` and z = `sum_("n" = 0)^oo cos^(2"n") theta, sin^(2"n") theta, 0 < theta < pi/2`, then show that xyz = x + y + z. [Hint: Use the formula 1 + x + x² + x³ + . . . = `1/(1 - x), where |x| < 1]

If tan² θ = 1 – k², show that sec θ + tan³ θ cosec θ = (2 – k²)^3/2. Also, find the values of k for which this result holds

If sec θ + tan θ = p, obtain the values of sec θ, tan θ and sin θ in terms of p

If cot θ(1 + sin θ) = 4m and cot θ(1 – sin θ) = 4n then prove that (m² – n²)² = m

If cosec θ – sin θ = a³ and sec θ – cos θ = b³, then prove that a²b² (a² + b²) = 1

Eliminate θ from the equations a sec θ – c tan θ = b and b sec θ + d tan θ = c

Identify the quadrant in which an angle given measure lies
25°

Identify the quadrant in which an angle given measure lies
825°