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REVISION SET- 01, , CLASS – XII, SUB – MATH, , TIME – 1 Hr., F.M. - 100, , * Evaluate the following:(1) cos[cos-1( 3/2) + 𝜋/6], 1, (2) 2 arc sin ½ + 3 arc tan(-1) + 2 arc cos(- ), 2, * Write the following in the simplest form :(3) cot-1 1 + 𝑠𝑖𝑛x + 1 − 𝑠𝑖𝑛𝑥, 1 + 𝑠𝑖𝑛x - 1 − 𝑠𝑖𝑛𝑥, (4) cos -1 1 + 𝑥 2 + 1, 2 1 + 𝑥2, * Prove that : (5) tan -11/2 + tan-1 1/3 = tan-1 3/5 + tan-1 ¼ = 𝜋/4, (6) 2 tan-11/2 + tan-1 1/7 = tan-1 31/17, (7) tan-1x + cot-1(1+x) = tan-1(1+x+x2), 1, y, (8) tan-1, + tan-1 2, = cot-1x, (9), , x+y, a−b, tan-1, 1+ab, -1 4, , (10) cos, (11), , 9𝜋, 8, 1, , 5, , 𝑥 +xy +1, -1 b−c, , + tan, , + cos, , 9, , 1, , 4, , 3, , = cos, , 13, 9, , - sin -1 = sin -1, -1, , (12) cos x =sin, 2, , 1+bc, -1 12, , + tan-1, , -1, , 4, -1 1−x, -1, , 2, , 2, , c−a, , 1+ca, -1 33, , =0, , 65, , 2, , 3, , = cos, -1, , -1 1+x, , 2, 𝜋, , -1, , = tan, , 1−𝑥 2, 1+𝑥, , (13) If tan x + tan y + tan z = , prove that yz + zx + xy = 1., 2, (14) Establish the algebraic relation between x,y,z if tan-1 x, tan-1 y,, tan-1 z are in A.P. and if further x,y,z are also in A.P. then prove, That x=y=z., * Solve for x :, , (15) cot-1 x + sin -1, , 1, 5, , =, , 𝜋, 4