HSC Arts (English Medium) ११ वीं कक्षा - Maharashtra State Board Question Bank Solutions

Find the other trigonometric functions:

If cot x = `3/4`, x lies in the third quadrant.

Find the other trigonometric functions:

If tan x = `(-5)/12`, x lies in the fourth quadrant.

If 2 sinA = 1 = `sqrt(2)` cosB and `pi/2` < A < `pi`, `(3pi)/2` < B < `2pi`, then find the value of `(tan"A" + tan"B")/(cos"A" - cos"B")`

If `sin"A"/3 = sin"B"/4 = 1/5` and A, B are angles in the second quadrant then prove that 4cosA + 3cosB = – 5.

If 2cos²θ − 11cosθ + 5 = 0 then find possible values of cosθ.

Answer the following:

State the signs of cosec 520°

Answer the following:

State the signs of cot 1899°

Answer the following:

State the signs of sin 986°

Answer the following:

State the quadrant in which θ lies if tan θ < 0 and sec θ > 0

Answer the following:

State the quadrant in which θ lies if sin θ < 0 and cos θ < 0

Answer the following:

State the quadrant in which θ lies if sin θ > 0 and tan θ < 0

Answer the following:

Which is greater sin(1856°) or sin(2006°)?

Answer the following:

Which of the following is positive? sin(−310°) or sin(310°)

Answer the following:

Show that 1 − 2sinθ cosθ ≥ 0 for all θ ∈ R.

Answer the following:

Show that tan²θ + cot²θ ≥ 2 for all θ ∈ R

Answer the following:

If sec θ = `sqrt(2)` and `(3pi)/2 < theta < 2pi` then evaluate `(1 + tantheta + "cosec"theta)/(1 + cottheta - "cosec"theta)`

Without expanding evaluate the following determinant:

`|(1, "a", "b" + "c"),(1, "b", "c" + "a"),(1, "c", "a" + "b")|`

Without expanding evaluate the following determinant:

`|(2, 3, 4),(5, 6, 8),(6x, 9x, 12x)|`

Without expanding evaluate the following determinant:

`|(2, 7, 65),(3, 8, 75),(5, 9, 86)|`

Prove that `|(x + y, y + z, z + x),(z + x, x + y, y + z),(y + z, z + x, x + y)| = 2|(x, y, z),(z, x, y),(y, z, x)|`