Class XII – Inverse Trigonometric Functions PYQ’s Q: Solve for x: sin^(-1)〖(1-x)-2 sin^(-1)〖x=π/2〗 〗 Previous Videos related to this chapter: Q10: Prove that cot^(-1)((√(1+sinx )+√(1-sinx ))/(√(1+sinx )-√(1-sinx )))=x/2, x∈(0,π/4): • Prove that 〖cot〗^(-1)((√(1+sinx )+√(1-si... Q12: Prove that 9π/8-9/4 sin^(-1)〖1/3〗=9/4 sin^(-1)〖(2√2)/3〗: • Prove that 9π/8-9/4 〖sin〗^(-1)〖1/3〗=9/4 ... Q13: Solve: 2 tan^(-1)(cosx )=tan^(-1)(2 cosecx ): • Solve: 2 〖tan〗^(-1)(cosx )=〖tan〗^(-1)(2... Q2: Find domain of y=sin^(-1)(2x): • Find domain of y=sin^(-1)(2x) Q7: y=sec^(-1) (2x+1): • Find domain of y=sec^(-1) (2x+1) Q9: y=sin^(-1)x+cos^(-1)x: • Find domain of y=〖sin〗^(-1)x+〖cos〗^(-1)x Q10: y=2 cos^(-1)2x+sin^(-1)x: • Find domain of y=2 cos^(-1)2x+sin^(-1)x Q285: Prove that cos{tan^(-1)(sin(cot^(-1)x ) ) }=√((1+x^2)/(2+x^2 )): • Prove that cos{〖tan〗^(-1)(sin(〖cot〗^(-1... 2025-26 INTRODUCTION TO INVERSE TRIGONOMETRIC FUNCTIONS: • INTRODUCTION TO INVERSE TRIGONOMETRIC FUNC... CONCEPT - SUM & DIFFERENCES OF 2 ITF’S: • CONCEPT - SUM & DIFFERENCES OF 2 ITF’S CONCEPT - RECIPROCAL PROPERTY: • CONCEPT - RECIPROCAL PROPERTY Q3: Find the domain of the following functions: sin^(-1)(2x-3): • Q3: Find the domain of the following funct... Q4: Find the domain of the following functions: sin^(-1)〖x^2 〗.: • Q4: Find the domain of the following funct... CONCEPT – TWICE OF ITF’s: • CONCEPT – TWICE OF ITF’s Q90: Prove that tan^2(sec^(-1)2 )+cot^2(cosec^(-1)3 )=11: • Q90: Prove that tan^2(sec^(-1)2 )+cot^2... Q95: Solve x: cos(tan^(-1)x )=sin(cot^(-1)〖3/4〗 ): • Q95: Solve x: cos(tan^(-1)x )=sin(cot^(... Q107: Evaluate cosec {cot^(-1) (-4/3)}: • Q107: Evaluate cosec {cot^(-1) (-4/3)} Q109: Prove that: sin^(-1) (-4/5)=tan^(-1) (-4/3)=cos^(-1) (-3/5)-π: • Q109: Prove that: sin^(-1) (-4/5)=tan^(-1)... Q118: If sin(sin^(-1)〖1/5〗+cos^(-1)x )=1 find the value of x.: • Q118: If sin(sin^(-1)〖1/5〗+cos^(-1)x )=... Q129: If (sin^(-1)x )^2+(cos^(-1)x )^2=(17n^2)/36, find the value of x: • Q129: If (sin^(-1)x )^2+(cos^(-1)x )^2=(... Q135: If tan^(-1)a+tan^(-1)b+tan^(-1)c=π, then prove that a+b+c=abc.: • Q135: If tan^(-1)a+tan^(-1)b+tan^(-1)c=... Q139: tan^(-1)〖(x-1)/(x+1)〗+tan^(-1)〖(2x-1)/(2x+1)〗=tan^(-1)〖23/36〗: • Q139: tan^(-1)〖(x-1)/(x+1)〗+tan^(-1)〖(2x... Q157: Find the value of tan^(-1)2x+tan^(-1)3x=π/4: • Q157: Find the value of tan^(-1)2x+tan^(-... Q165: Prove that: sin^(-1)〖12/13〗+cos^(-1)〖4/5〗+tan^(-1)〖63/16〗=π: • Q165: Prove that: sin^(-1)〖12/13〗+cos^(-1... Q191: Prove that: 2 tan^(-1)〖1/2〗+tan^(-1)〖1/7〗=tan^(-1)〖31/17〗: • Q191: Prove that: 2 tan^(-1)〖1/2〗+tan^(-1... Q196: Prove that 9π/8-9/4 sin^(-1)〖1/3〗=9/4 sin^(-1)〖(2√2)/3〗: • Q196: Prove that 9π/8-9/4 sin^(-1)〖1/3〗=... Q209: Solve for x: 2 tan^(-1)(sinx )=tan^(-1)(2 secx );x≠π/2: • Q209: Solve for x: 2 tan^(-1)(sinx )=tan... Q: Show that tan(π/4+1/2 cos^(-1)〖a/b〗 )+tan(π/4-1/2 cos^(-1)〖a/b〗 )=2: • Q: Show that tan(π/4+1/2 cos^(-1)〖a/b〗 ... Q: Evaluate: cos(2 tan^(-1)2 )+sin(2 tan^(-1)3 ): • Q: Evaluate: cos(2 tan^(-1)2 )+sin(2 ta... Q: Evaluate tan(2 tan^(-1)〖1/5〗-π/4): • Q: Evaluate tan(2 tan^(-1)〖1/5〗-π/4) Q: Solve:(tan^(-1)x )^2+(cot^(-1)x )^2=(5π^2)/8: • Q: Solve:(tan^(-1)x )^2+(cot^(-1)x )^2=(... Q213: Solve: sin^(-1)x+sin^(-1)(1-x)=cos^(-1)x: • Q213: Solve: sin^(-1)x+sin^(-1)(1-x)=cos... Q291: Find the value of tan^(-1)[2 cos(2 sin^(-1)〖1/2〗 ) ]+tan^(-1)1: • Q291: Find the value of tan^(-1)[2 cos(2... Q: sin^(-1)[π/3+sin^(-1)(1/2) ]= a) 1 b) 1/2 c) 1/3 d) 1/4 • sin^(−1)[𝜋/3+sin^(−1)(1/2) ]= a) ... Q:If tan^(-1)〖x=y〗, then • Q:If tan^(-1)〖x=y〗, then a) -1 greate... a) -1 greater than y greater than 1 b) -π/2≤y≤π/2 c) -π/2 greater than y greater than π/2 d) y∈{-π/2,π/2} Q: sin[π/3-sin^(-1)(-1/2) ]= • Q: sin[𝜋/3−sin^(−1)(−1/2) ]=a) 1/2 b) 1... a) 1/2 b) 1/3 c) -1 d) 1 Q: sin(tan^(-1)x )= ; |x| greater than 1 a) x/√(1-x^2 ) b) 1/√(1-x^2 ) c) 1/√(1+x^2 ) d) x/√(1+x^2 ) • Q: sin(tan^(−1)𝑥 )= ; |𝑥| greater th... Q: Simplest form of tan^(-1)〖[(√(1+cosx)+√(1-cosx))/(√(1+cosx)-√(1-cosx))];π greater than x greater than 3π/2 〗 • Simplest form of tan^(-1)〖[(√(1+cosx)+√(1... a) π/4-x/2 b) 3π/2-x/2 c) -x/2 d) π-x/2 Q: Simplify: cot^(-1)〖1/√(x^2-1)〗 for x is less than-1 • Simplify: cot^(-1)〖1/√(x^2-1)〗 for x le... Q: If 4 sin^(-1)〖x+cos^(-1)〖x=π, find x〗 〗 • If 4 sin^(−1)〖𝑥+cos^(−1)〖𝑥=𝜋, 𝑓𝑖𝑛𝑑 𝑥〗 〗 Q: Prove that: 3 cos^(-1)〖x=cos^(-1)〖[4x^3-3cosx];x∈[1/2, 1]〗 〗 • Q: Prove that:3 cos^(−1)〖𝑥=cos^(−1)〖[4𝑥^... Q: Express sin^(-1)〖((sinx+cosx)/√2); -π/4 less than x less than π/4 〗 in its simplest form • Express sin^(−1)〖((𝑠𝑖𝑛𝑥+𝑐𝑜𝑠𝑥)/√2); −𝜋/4 ... Q: Solve for x: tan^(-1)〖((1-x)/(1+x))=1/2 tan^(-1)〖x; x less than 0〗 〗 • Solve for x: tan^(-1)〖((1-x)/(1+x))=1/2 ... Q: If sin[cot^(-1)〖(x+1)]=cos(tan^(-1)x ); find x〗 • If sin[cot^(−1)〖(𝑥+1)]=cos(tan^(−1)𝑥 )... Q: Prove that: 2 tan^(-1)〖(1/5)+sec^(-1)〖((5√2)/7)+2 tan^(-1)〖(1/8)=π/4〗 〗 〗 • Prove that:2 tan^(−1)〖(1/5)+sec^(−1)〖((5... #cbse #icse #boards #8th #9th #10th #foundation #competition #iit #jee #Advanced #mains #ntse #olympiads #exams #examination #achiever #topper #zenith #zenithinstituteofmathematics #indersir #ludhiana #modelgram #bestmathscoaching #besttutorials #besttuition #bestinludhiana #mathtricks #viii #ix #x #xi #xii #important #excellent #question #exponents #powers #bases #lawsofexponents #numbersystem #rationalization #ITF #Inverse #inversetrigonometricfunctions