Differentiation Of Different Function | Chapter 03 | Lecture 02 Notes For Polytechnic

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Applied Mathematics - ll : Differentiation Of Different Function|Chapter 03 | Lecture 02 Notes For Polytechnic

( Lecture 02 )

Hey Everyone, How are you ... Today I will tell you How to Differentiate Of Function Using Trigonometry Transformation , Which is lecture 02 of Chapter 03 Differentiation Of Different Function Applied Mathematics 2 

- This Lecture Is Very Important For Your Calculus .

Lecture - 02 ( Topics ) :

1 ) Differentiation Of Function By  Trigonometrical transformation

2 ) Trigonometry Formula Related Basic Questions

3 ) Trigonometry Inverse Formula based Questions

4 ) Some Important Substitution Based Questions

5 ) Lecture Related Notes .

( Overview )

- Trigonometry Formula Related Basic Questions

1) Sin2x = 2Sinxcosx

2) Sin2x = 2tanx / 1 + tan²x

3) Cos2x = Cos²x - Sin²x 

4) Cos2x = 2Cos²x - 1

5) Cos2x = 1 - Sin²x

6) Cos2x = 1 - tan²x / 1 + tan²x

7) tan2x = 2tanx / 1 - tan²x 

8) Sin3x = 3Sinx - 4Sin³x

9) Cos3x = 4Cos³x - 3Cosx

10) tan3x = 3tanx - tan³x / 1 - 3tan²x 

- Note ; 

1 ) Sin-¹ ( Sinx ) = x

2 ) Cos-¹ ( Cosx ) = x

3 ) tan-¹ ( tanx ) = x

- Where x belongs to range of Inverse of trigonometry

( Imp Formulas )

Some Important Questions ;

Questions 01 ; 

Differentiate Sin-¹ (3x - 4x³) , w.r.t x 

Solution : View In This Page

( Question 01 )

Question 02 ;

Differentiate y = tan-¹ ( 2x / 1 - x² ) w.r.t, x 

Solution : View On This Page 

( Question 02 )

Question 03 ; 

Differentiate y = tan-¹ {✓ 1 - Cosx / 1 + Cosx}

Solution : View On This Page 

( Question 03 )

( Question 03 )

Question 04 ;

Differentiate y = tan-1 { ✓ 1 + x² - 1 / x } 

Solution : View On This Page 

( Question 04 )

Question 05 :

If y = tan-¹{ acosx - bsinx / bcosx + asinx }, Find dy/dx

Solution : View In This Page 

( Question 05 )

- Some Trigonometry Inverse Formulas

1 ) tan-¹x + tan-¹y     = tan-¹ { ( x + y ) / 1 - xy }

2 ) tan-¹x - tan-¹y      = tan-¹ { ( x - y ) / 1 + xy }

3 ) Sin-¹x +Cos-¹y      = π/2

4 ) tan-¹x + Cot-¹y     = π/2

5 ) Cosec-¹x + Sec-¹y = π/2 

Some Important Questions 

Question 01 ) 

Differentiate tan-¹ ( a + x / 1 - ax ) , w.r .t x 

Solution : View On This Page

( Question 01 )

Question 02 ) 

Differentiate tan -¹ { Cosx + Sinx / Cosx - Sinx } w.r.t. x.

Solution : View On This Page 

( Question 02 )

- Some Important Substitution Formula ;

1 ) a² - x²  then , x = aSiny Or X = aCosy

2 ) a² + x² then,  x = atany Or X = aCoty

3 ) x² - a²  then,  X = aSecy Or x = a Cosecy

Some Important Questions :

Question 01 ) 

Differentiate Sec -¹ ( a / ✓ a² - x² )

Solution : View On This Page 

Question 02 ) 

Differentiate Sin -¹ { x /✓ x² + a² } w.r.t, x

Solution : View On This Page 

( Question 1 & 2 )

Lecture Related Question ;

 ( LRQ )

Chapter 03 | Lecture 02 Full Notes ;

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