HSC Arts Class 12 - Tamil Nadu Board of Secondary Education Question Bank Solutions

Prove that `sin^-1  3/5 - cos^-1  12/13 = sin^-1  16/65`

Prove that `tan^-1x + tan^-1y + tan^-1z = tan^-1[(x + y + z - xyz)/(1 - xy - yz - zx)]`

If tan^–1x + tan^–1y + tan^–1z = π, show that x + y + z = xyz

Simplify: `tan^-1  x/y - tan^-1  (x - y)/(x + y)`

Solve: `sin^-1  5/x + sin^-1  12/x = pi/2`

Solve: `tan^-1x = cos^-1  (1 - "a"^2)/(1 + "a"^2) - cos^-1  (1 - "b"^2)/(1 + "b"^2), "a" > 0, "b" > 0`

Solve: `2tan^-1 (cos x) = tan^-1 (2"cosec"  x)`

Solve: `cot^-1 x - cot^-1 (x + 2) = pi/12, x > 0`

Find the number of solutions of the equation `tan^-1 (x - 1) + tan^-1x + tan^-1(x + 1) = tan^-1(3x)`

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If `sin^-1x + sin^-1y = (2pi)/3` ; then `cos^-1x + cos^-1y` is equal to

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`sin^-1  3/5 - cos^-1  13/13 + sec^-1  5/3 - "cosec"^-1  13/12` is equal to

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`tan^-1 (1/4) + tan^-1 (2/9)` is equal to

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`sin^-1 (tan  pi/4) - sin^-1 (sqrt(3/x)) = pi/6`. Then x is a root of the equation

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sin^–1(2 cos²x – 1) + cos^–1(1 – 2 sin²x) =

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If `cot^-1(sqrt(sin alpha)) + tan^-1(sqrt(sin alpha))` = u, then cos 2u is equal to

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The equation tan^–1x – cot^–1x = `tan^-1 (1/sqrt(3))` has

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If `sin^-1x + cot^-1 (1/2) = pi/2`, then x is equal to

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sin(tan^–1x), |x| < 1 is equal to

Find the equation of the plane passing through the line of intersection of the planes `vec"r"*(2hat"i" - 7hat"j" + 4hat"k")` = 3 and 3x – 5y + 4z + 11 = 0, and the point (– 2, 1, 3)

Find the equation of the plane passing through the line of intersection of the planes x + 2y + 3z = 2 and x – y + z = 3 and at a distance `2/sqrt(3)` from the point (3, 1, –1)