10:[["$","title","0",{"children":"CUET Mathematics - _/6^/3 tan x/tan x + cot x dx is equal to | PYQs + Solutions | AfterBoards"}],["$","meta","1",{"name":"description","content":"undefined The integrand can be simplified: x/ x + x Since x = 1/ x: x/ x + x = x x + 1/ x

Multiply both numerator and denominator by x: x x( x + 1/ x) x = ^2 x/^2 x + 1

Using the identity ^2 x + 1 = ^2 x: ^2 x/^2 x + 1 = ^2 x/^2 x Since x = x/ x and x = 1/ x: ^2 x/^2 x = ^2 x/^2 x1/^2 x = ^2 x The integral becomes: _/6^/3 ^2 x dx

Using the identity ^2 x = 1 - 2x/2: _/6^/3 ^2 x dx = _/6^/3 1 - 2x/2 dx = 1/2 _/6^/3 (1 - 2x) dx

Integrating: = 1/2 [x - 2x/2]_/6^/3

Evaluating at the limits: At x = /3: (2/3) = sqrt(3)2 At x = /6: (/3) = sqrt(3)2 = 1/2 [(/3 - sqrt(3)/22) - (/6 - sqrt(3)/22)] The sqrt(3)/22 terms cancel: = 1/2 [/3 - /6] = 1/2 [2 - /6] = 1/2 /6 = /12 Therefore, the answer is /12."}],["$","link","2",{"rel":"manifest","href":"https://www.afterboards.in/manifest.json","crossOrigin":"$undefined"}],["$","meta","3",{"name":"keywords","content":"CUETMAT,MAT,Calculus,Integrals"}],["$","meta","4",{"name":"robots","content":"index, follow"}],["$","meta","5",{"name":"category","content":"education"}],["$","meta","6",{"name":"google-site-verification","content":"google"}],["$","meta","7",{"property":"og:title","content":"CUET Mathematics - _/6^/3 tan x/tan x + cot x dx is equal to | PYQs + Solutions"}],["$","meta","8",{"property":"og:description","content":"undefined The integrand can be simplified: x/ x + x Since x = 1/ x: x/ x + x = x x + 1/ x

Multiply both numerator and denominator by x: x x( x + 1/ x) x = ^2 x/^2 x + 1

Using the identity ^2 x + 1 = ^2 x: ^2 x/^2 x + 1 = ^2 x/^2 x Since x = x/ x and x = 1/ x: ^2 x/^2 x = ^2 x/^2 x1/^2 x = ^2 x The integral becomes: _/6^/3 ^2 x dx

Using the identity ^2 x = 1 - 2x/2: _/6^/3 ^2 x dx = _/6^/3 1 - 2x/2 dx = 1/2 _/6^/3 (1 - 2x) dx

Integrating: = 1/2 [x - 2x/2]_/6^/3

Evaluating at the limits: At x = /3: (2/3) = sqrt(3)2 At x = /6: (/3) = sqrt(3)2 = 1/2 [(/3 - sqrt(3)/22) - (/6 - sqrt(3)/22)] The sqrt(3)/22 terms cancel: = 1/2 [/3 - /6] = 1/2 [2 - /6] = 1/2 /6 = /12 Therefore, the answer is /12."}],["$","meta","9",{"property":"og:url","content":"https://www.afterboards.in/past-year-questions/cuet-mathematics/2025/slot-3/50"}],["$","meta","10",{"property":"og:site_name","content":"AfterBoards | CUET Mathematics Preparation"}],["$","meta","11",{"property":"og:image","content":"https://www.afterboards.in/pyp/AfterBoards%20CUET%20Past%20Year%20Papers%20with%20Solutions.webp"}],["$","meta","12",{"property":"og:type","content":"website"}],["$","meta","13",{"name":"twitter:card","content":"summary_large_image"}],["$","meta","14",{"name":"twitter:site","content":"afterboards.in"}],["$","meta","15",{"name":"twitter:title","content":"CUET Mathematics - _/6^/3 tan x/tan x + cot x dx is equal to | PYQs + Solutions"}],["$","meta","16",{"name":"twitter:description","content":"undefined The integrand can be simplified: x/ x + x Since x = 1/ x: x/ x + x = x x + 1/ x

Multiply both numerator and denominator by x: x x( x + 1/ x) x = ^2 x/^2 x + 1

Using the identity ^2 x + 1 = ^2 x: ^2 x/^2 x + 1 = ^2 x/^2 x Since x = x/ x and x = 1/ x: ^2 x/^2 x = ^2 x/^2 x1/^2 x = ^2 x The integral becomes: _/6^/3 ^2 x dx

Using the identity ^2 x = 1 - 2x/2: _/6^/3 ^2 x dx = _/6^/3 1 - 2x/2 dx = 1/2 _/6^/3 (1 - 2x) dx

Integrating: = 1/2 [x - 2x/2]_/6^/3

CUET Mathematics 2025 14 May Shift 1 PYQs

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