HSC Science कक्षा ११ - Tamil Nadu Board of Secondary Education Question Bank Solutions

Identify the quadrant in which an angle given measure lies
328°

Identify the quadrant in which an angle given measure lies
– 230°

For each given angle, find a coterminal angle with measure of θ such that 0° ≤ θ < 360°
395°

For each given angle, find a coterminal angle with measure of θ such that 0° ≤ θ < 360°
525°

For each given angle, find a coterminal angle with measure of θ such that 0° ≤ θ < 360°
1150°

For each given angle, find a coterminal angle with measure of θ such that 0° ≤ θ < 360°
– 270°

For each given angle, find a coterminal angle with measure of θ such that 0° ≤ θ < 360°
– 450°

If a cos θ − b sin θ = c, show that a sin θ + b cos θ = `+-  sqrt("a"^2 + "b"^2 - "c"^2)`

If sin θ + cos θ = m, show that cos⁶θ + sin⁶θ = `(4 - 3("m"^2 - 1)^2)/4`, where m² ≤ 2

If `(cos^4α)/(cos^2β) + (sin^4α)/(sin^2β)` = 1, prove that sin⁴α + sin⁴β = 2 sin²α sin²β

If `(cos^4alpha)/(cos^2beta) + (sin^4alpha)/(sin^2beta)` = 1, prove that `(cos^4beta)/(cos^2alpha) + (sin^4beta)/(sin^2alpha)` = 1

If y = `(2sinalpha)/(1 + cosalpha + sinalpha)`, then prove that `(1 - cosalpha + sinalpha)/(1 + sinalpha)` = y

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

Choose the correct alternative:
The maximum value of `4sin^2x + 3cos^2x + sin   x/2 + cos  x/2` is

Choose the correct alternative:
Which of the following is not true?