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Simplifying ITF questions using substitution and Trigonometry formulas
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This lesson takes up problems involving simplification of ITF using substitution and Trigonometry formulas

## Vineet Loomba is teaching live on Unacademy Plus

Vineet Loomba
IITian | No. 1 Educator in IIT-JEE | 6 Million Minutes Watch Time | 8+ Years Experience | Youtube: Maths Wallah | vineetloomba.com

U
kya aap only mathematics k questions ki hi practice karaenge ya fir chemistry and physics ki bhi
Shivam Gupta
a year ago
maths
sir we have substitution a^2+x^2 for this x=atanQ but if we have expression under root of a^2 =^2 then also can we use this substitution
sir 6:30 par substitution x=acos2thetha chahiye but aapne acos thetha kiya hai why
Vineet Loomba
3 months ago
Aisa fix nhi hota ki 2Q he krna h ..Q bhi kr skte h angles half angle ban jaene bs ..ans same rhega
Om Kendre
3 months ago
ok
sir around 7:48 in the given problem it is given that -a<x<a and on putting x=acos(theta) my answer is coming π<(theta)<0 but yours is 0<(theta)<π I am confused help me sir
Vineet Loomba
4 months ago
In writing inequality lower value come on left hand side right ... It will from 0 to pie and not pie to zero
Top10Fab
4 months ago
thanks sir
at 7 :18 -a<x<a ka concept kya hai
at 6:39 why are we putting x=acos(theta)..instead of x=acos2(theta)..as you have told in the earlier slide
Vineet Loomba
4 months ago
It is one and the same thing ..u can try different substitution ..ans will be same
1. INVERSE TRIGONOMETRIC FUNCTIONS FoR SURe SHoT SUcCESS IN JEE MAIN AND ADVANCED (IIT-JEE) JEE MAIN RANK BOOSTER COURSE PREPARED BY ER. VINEET LOOMBA ITIAN IIT-JEE MENTOR

2. 100% SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) SPECIAL ANNOUNCEMENT Share useful links and advice with your learners... CRASH COURSE FOR JEE MAIN 2019 (JANUARY SESSION) Find courses & lessons 735 Courses IIT JEE 2,521 Courses Str Chemistry 797 Courses Details in Plus Tab wwEest HINDI Home My Library Plus Profile SUCCESS IN JEE MAIN ER. VINEET LoOMBA (IIT RooRKEE)

3. 100% SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) ABOUT ME B. Tech. From IIT Roorkee IIT-JEE Mentor Since 2010. * Many of my students are pursuing courses in IITs, NITs, BITs etc unacademy Currently running my own Coaching Institute for JEE Main and Advanced Search vineet loomba unacademy on GOOGLE

4. 100% SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) SOLVED EXAMPLE: (A) x=1 The value of x which satisfies tan- 2x + tan-' 3x =-is: 4 (B) x= (C) x= (D) None of these rs- SOLUTION : (C) We have, tan-1 2x + tan-I 3x 4 2x +3 = tan-11, if 6x2 <1 tan l-2x 3x if 6r2 < 1 6x2 + 5x-1=0 and (6x-1)(x +1)-0 and SUCCESS IN EE MAIN ER. VINEET LOOMBA (IIT RooRKEe)

5. 100% SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) SUBSTITUTION TABLE: Experssion Substitution a + x x=atan or, x = a cot 2 a2 x= a sec or, x = a cosec a+ x x = a cos 2 a t x a-x a + r x-= a- cos 2 a + x SUCCESS IN EE MAIN ER. VINEET LOOMBA (IIT RooRKEe)

6. 100% SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) SOLVED EXAMPLE: The simplest form of tan- l- 1 + cos x (A) -x/2 x/2 (C) x (D) None of these SOLUTION: (AB) 2 sin +) | 1-cos x ) = tan 1 + cos x -1 We have, tan tantan tan 2 cos* tantan -1 | if - <x<b |tan- tan tan tan tan , tan if 0<x< SUCCESS IN EE MAIN ER. VINEET LOOMBA (IIT RooRKEe)

7. 100% SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) The simplest form of ExAMPLE: tan a tx (A) cos-1 (B) 1 (D) None of these SOLUTION: (B) Substituting x = a cos , we have tan tan a+ x a+acos 1 + cos 2 sin 2- = tan ' | | tan = tan-1(tan =-=-cos SUCCESS IN EE MAIN ER. VINEET LOOMBA (IIT RooRKEe)

8. 100% SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) SoLved EXAMPLE: The simplest form of tan - is cos x + Sin x 4 4 _x (D) 2 (C) 4 SOLUTION: (A) 1-tan x 1 + tan x we have, tan cos x + Sin _ < x <--> 0 <-- 4 as 4 4 SUCCESS IN EE MAIN ER. VINEET LOOMBA (IIT RooRKEe)

9. 100% SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) SOLVED The simplest form of EXAMPLE: ,0<x<-, is : l +cosx -cos r 1t(D) None of these C) 2 SOLUTION: (C) 2 cos"-+ /2 sin We have, tan tan 1 + cos x-cos x 2X2 2 sin 2 cos coS-+sin- s tan COSsin 1+tan tan-1 21-tan-l tan-+- tan = 1-tan SUCCESS IN EE MAIN ER. VINEET LOOMBA (IIT RooRKEe)

10. 100% SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) SOLVED EXAMPLE: The simplest form of (A) 2 2(D) None of these (B) Cos SOLUTION: (B) Putting cos 20, we have tan 1 + cos 2 -1-cos 2 -| | cos0+ sin cos -sin = tan-1 j + tan 1-tan tan 4 4 SUCCESS IN EE MAIN ER. VINEET LOOMBA (IIT RooRKEe)

11. 100% SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) coS-sin- coS +sin- coS- sin = tan coS+Sin- coS-+ sin- l-tan- tan tan-1 : tan 1 + tan SUCCESS IN EE MAIN ER. VINEET LOOMBA (IIT RooRKEe)