Q118: If sin(sin^(-1)〖1/5〗+cos^(-1)x )=1 find the value of x.
Class XII - Inverse Trigonometric Functions Q118: If sin(sin^(-1)〖1/5〗+cos^(-1)x )=1 find the value of x. Previous Videos related to this chapter: Q: Evaluate tan(2 tan^(-1)〖1/5〗-π/4): • Evaluate tan(2 tan^(−1)〖1/5〗 − 𝜋/4) Q117: IF 〖tan〗^(-1) x-〖cot〗^(-1)x=〖tan〗^(-1)〖1/√3〗, Find x • IF tan inverse x - cot inverse x = tan inv... Q124: If (〖tan〗^(-1)x )^2+(〖cot〗^(-1)x )^2=(5π^2)/8, then find x • If (〖tan〗^(-1)x )^2+(〖cot〗^(-1)x )^2=(5π... Q125, 126: Evaluate: sin(〖tan〗^(-1)x+〖tan〗^(-1)〖1/x〗 ) • Evaluate: sin(〖tan〗^(-1)x+〖tan〗^(-1)〖1/... Q135: Find the greatest and least values of (〖sin〗^(-1)x )^2+(〖cos〗^(-1)x )^2: • Find the greatest and least values of (〖si... Q: Evaluate cos(2 tan^(-1)2 )+sin(2 tan^(-1)3 ): • Evaluate cos(2 tan^(−1)2 )+sin(2 tan^(... COMPLETE NCERT EXERCISE 2.1 | ONE SHOT VIDEO: • COMPLETE NCERT EXERCISE 2.1 | ONE SHOT VIDEO Q1: Prove that 3 〖sin〗^(-1)x=〖sin〗^(-1)(3x-4x^3 ): • Prove that 𝟑 〖𝐬𝐢𝐧〗^(−𝟏)𝒙=〖𝐬𝐢𝐧〗^(−𝟏)(𝟑𝒙−𝟒... Q2: Prove 3 〖cos〗^(-1)x=〖cos〗^(-1)(4x^3-3x);x∈[1/2,1]: • Prove 3 〖cos〗^(-1)x=〖cos〗^(-1)(4x^3-3x);... Q3: Write in simplest form: • Write in simplest form:〖tan〗^(-1)〖(√(1+x^... 〖tan〗^(-1)〖(√(1+x^2 )-1)/x〗 Q4: Write in simplest form: • Write in simplest form:〖𝐭𝐚𝐧〗^(−𝟏)√((𝟏−𝐜𝐨𝐬... 〖tan〗^(-1)√((1-cosx)/(1+cosx )), 0 x π Q5: Write in simplest form: • Write in simplest form:〖tan〗^(-1)((cosx-... 〖tan〗^(-1)((cosx-sinx)/(cosx+sinx )), -π/4 x 3π/4 Q6: Write in simplest form: • Write in simplest form:〖tan〗^(-1)〖x/√(a^2... 〖tan〗^(-1)〖x/√(a^2-x^2 )〗, |x| a Q7: Write in simplest form: • Write in simplest form:〖𝐭𝐚𝐧〗^(−𝟏)〖(𝟑𝒂^𝟐 𝒙... 〖tan〗^(-1)〖(3a^2 x-x^3)/(a^3-3ax^2 )〗, a 0;- Q8: Find the value of: • Find the value of:〖𝐭𝐚𝐧〗^(−𝟏)[𝟐 𝐜𝐨𝐬(𝟐 〖𝐬𝐢... 〖tan〗^(-1)[2 cos(2 〖sin〗^(-1)〖1/2〗 ) ] Q9: Find the value of: • Find the value of:tan〖1/2 [〖sin〗^(-1)〖2x... tan〖1/2 [〖sin〗^(-1)〖2x/(1+x^2 )〗+〖cos〗^(-1)〖(1-y^2)/(1+y^2 )〗 ]〗, |x| 1, y 0 & xy 1 Q10: Find the value of: • Find the value of:〖sin〗^(-1)[sin〖2π/3〗 ] 〖sin〗^(-1)[sin〖2π/3〗 ] Q11: Find the value of: • Find the value of:〖𝐭𝐚𝐧〗^(−𝟏)[𝐭𝐚𝐧〖𝟑𝝅/𝟒〗 ] 〖tan〗^(-1)[tan〖3π/4〗 ] Q12: Find the value of: • Find the value of:tan(〖sin〗^(-1)〖3/5〗+〖c... tan(〖sin〗^(-1)〖3/5〗+〖cot〗^(-1)〖3/2〗 ) Q13: Find the value of: • Find the value of:〖𝐜𝐨𝐬〗^(−𝟏)[𝐜𝐨𝐬〖𝟕𝝅/𝟔〗 ] 〖cos〗^(-1)[cos〖7π/6〗 ] Q14: Find the value of: • Find the value of: sin(π/3-〖sin〗^(-1)[-1... sin(π/3-〖sin〗^(-1)[-1/2] ) Q15: Find the value of: • Find the value of:〖tan〗^(-1)√3-〖cot〗^(-1)... 〖tan〗^(-1)√3-〖cot〗^(-1)(-√3) Q1: Find the value of: 〖cos〗^(-1)(cos〖13π/6〗 ): • Find the value of: 〖cos〗^(-1)(cos〖13π/6〗 ) Q2: Find the value of: 〖tan〗^(-1)(tan〖6π/6〗 ): • Find the value of: 〖tan〗^(-1)(tan〖6π/6〗 ) Q3: Prove that 2 〖sin〗^(-1)〖3/5〗=〖tan〗^(-1)〖24/7〗: • Prove that 2 〖sin〗^(-1)〖3/5〗=〖tan〗^(-1)〖... Q4: Prove that 〖sin〗^(-1)〖8/17〗+〖sin〗^(-1)〖3/5〗=〖tan〗^(-1)〖77/36〗: • Prove that 〖sin〗^(-1)〖8/17〗+〖sin〗^(-1)〖3... Q5: Prove that 〖cos〗^(-1)〖4/5〗+〖cos〗^(-1)〖12/13〗=〖cos〗^(-1)〖33/65〗: • Prove that 〖cos〗^(-1)〖4/5〗+〖cos〗^(-1)〖12... Q6: Prove that 〖cos〗^(-1)〖12/13〗+〖sin〗^(-1)〖3/5〗=〖sin〗^(-1)〖56/65〗: • Prove that 〖cos〗^(-1)〖12/13〗+〖sin〗^(-1)〖... Q7: Prove that 〖tan〗^(-1)〖63/16〗=〖sin〗^(-1)〖5/13〗+〖cos〗^(-1)〖3/5〗: • Prove that 〖tan〗^(-1)〖63/16〗=〖sin〗^(-1)〖... Q8: Prove that 〖tan〗^(-1)〖1/5〗+〖tan〗^(-1)〖1/7〗+〖tan〗^(-1)〖1/3〗+〖tan〗^(-1)〖1/8〗=π/4: • Prove that 〖tan〗^(-1)〖1/5〗+〖tan〗^(-1)〖1/... 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... Q11: Prove that 〖tan〗^(-1)((√(1+x)-√(1-x))/(√(1+x)+√(1-x)))=π/4-1/2 〖cos〗^(-1)x, -1/√2≤x≤1: • Prove that 〖tan〗^(-1)((√(1+x)-√(1-x))/(√(... 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... Q14: Solve: 〖tan〗^(-1)〖(1-x)/(1+x)〗=1/2 〖tan〗^(-1)x, (x 0): • Solve: 〖tan〗^(-1)〖(1-x)/(1+x)〗=1/2 〖tan〗... 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 Q284: Prove that 〖tan〗^(-1){(√(1+x^2 )+√(1-x^2 ))/(√(1+x^2 )-√(1-x^2 ))}=π/4+1/2 〖cos〗^(-1)〖x^2 〗;-1 x 1: • Prove that 〖tan〗^(-1){(√(1+x^2 )+√(1-x^2 ... Q285: Prove that cos{〖tan〗^(-1)(sin(〖cot〗^(-1)x ) ) }=√((1+x^2)/(2+x^2 )): • Prove that cos{〖tan〗^(-1)(sin(〖cot〗^(-1... 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: • Q3: Find the domain of the following funct... Q4: • Q4: Find the domain of the following funct... CONCEPT – TWICE OF ITF’s: • CONCEPT – TWICE OF ITF’s Q90: • Q90: Prove that tan^2(sec^(-1)2 )+cot^2... Q95: • Q95: Solve x: cos(tan^(-1)x )=sin(cot^(... Q107: • Q107: Evaluate cosec {cot^(-1) (-4/3)} Q109: • Q109: Prove that: sin^(-1) (-4/5)=tan^(-1)... Q113: • Q113: If -1≤x, y≤1 such that sin^(-1)x+si... #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
