TRIGONOMETRY ALL FORMULAS

 

• SinA = P/H
• CosA = B/H
• TanA = P/B
• CosecA = H/P
• SecA = H/B
• CotA = B/P

Reciprocal Relation of Trigonometric formulas for class 10

1. Cosec A   =  1/Sin A

2. Sin A        =  1/Cosec A

3. Sec A       =  1/Cos A

4. Cos A       =  1/Sec A

5. Cot A        =  1/Tan A 

6. Tan A        =  1/Cot A

 

Trigonometric Angles

Angles	0°	30°	45º	60°	90°
Sin θ	0	1/2	1/√2	√3/2	1
Cos θ	1	√3/2	1/√2	1/2	0
Tan θ	0	1/√3	1	√3	∞
Cosec θ	∞	2	√2	2/√3	1
Sec θ	1	2/√3	√2	2	∞
Cot θ	∞	√3	1	1/√3	0

 

Trigonometric ratios of complementary Angles

1. Sin (90-A)       = Cos A

2. Cos (90-A)      = Sin A

3. Tan (90-A)       = Cot A

4. Cot (90-A)       = Tan A

5. Sec (90-A)       = Cosec A

6. Cosec (90-A)   = Sec A

 

Some other important class 10 Trigonometry formula

1. TanA x CotA = 1

2. SinA x CosecA = 1

3. CosA x SecA =1

4. TanA = SinA/CosA

4. CotA = CosA/SinA

 

Trigonometry identity

An equation involving trigonometric ratios of an angle is called a trigonometric identity if it is true for all values of the angle.

Trigonometric identities are useful whenever an expression or equation involves trigonometric functions. Trigonometric identities are true for every value of the variables occurring on both sides of the equation. Geometrically, these identities include some trigonometric functions (e.g. sine, cosine, and tangent) of one or more angles.

Trigonometric Identity Formula for Class 10

1. Sin2A + Cos2A = 1

2. Sec2A + Tan2A = 1

3. Cosec2A + Sec2A = 1

Advance Formula of trigonometry class 10

1. Sin (A+B) = SinA x CosB + CosA x SinB

2. Sin (A-B) = SinA x CosB – CosA x SinB

3. Cos (A+B) = CosA x CosB – SinA x SinB

4. Cos (A-B) = CosA x CosB + SinA x SinB

5. Tan (A+B) = (TanA + TanB)/(1 – TanA x TanB)

6. Tan (A-B) = (TanA – TanB)/(1 + TanA x TanB)

7. Sin2A = 2SinACosA

                            OR

        = 2TanA/(1+Tan2A)

 

8. Cos2A = Cos2A – Sin2A 

                    OR

           = 1 – 2Sin2A

                     OR

           = 2Cos2A – 1

                    OR

    = (1-Tan2A)/(1+Tan2A)

                                   

 

9. Sin3A = 3SinA – 4Sin3A

 

10. Cos3A = 4Cos3A – 3CosA

 

11.Tan3A = (3TanA-4Tan2A)/(1+3Tan2A)

 

12. SinA x Sin2A X Sin4A = ¼ Sin3A

 

13. CosA x Cos2A x Cos4A = ¼ Cos3A

 

14. TanA x Tan2A x Tan4A = Tan3A

@Jbc , #BadaJoke_GroupOf_SocialHandles

Trigonometry [TRICKS TO LEARN] EXERCISE 8.1

 Pandit Badri Prasad 

Har Har Bol

Sona Chandi Tol

Sin= P/H

Cos= B/H

Tan=P/B

This are the tricks to learn the simple TRIGONOMETRY. 

_____________________________________________________________

EXERCISE 8.1 

MADE SIMPLE 

Maths Question 1.
In ∆ABC right angled at B, AB = 24 cm, BC = 7 cm. Determine:
(i) sin A, cos A
(ii) sin C, cos C
Solution:

 Maths Question 2.
In given figure, find tan P – cot R.
Solution:

Maths Question 3.
If sin A = 34 , calculate cos A and tan A.
Solution:

Maths Question 4.
Given 15 cot A = 8, find sin A and sec A.
Solution:

 Maths Question 5.
Given sec θ = 1312 , calculate all other trigonometric ratios.
Solution:

Maths Question 6.
If ∠A and ∠B are acute angles such that cos A = cos B, then show that ∠A = ∠B.
Solution:

Maths Question 7.
If cot θ = 78, evaluate:
(i) (1+sinθ)(1−sinθ)(1+cosθ)(1−cosθ)
(ii) cot²θ
Solution:

Maths Question 9.
In triangle ABC, right angled at B, if tan A = 1√3, find the value of:
(i) sin A cos C + cos A sin C
(ii) cos A cos C – sin A sin C
Solution:

 Maths Question 10.
In ΔPQR, right-angled at Q, PR + QR = 25 cm and PQ = 5 cm. Determine the values of sin P, cos P and tan P.
Solution:

Maths Question 11.
State whether the following statements are true or false. Justify your answer.
(i) The value of tan A is always less than 1.
(ii) sec A = 125 for some value of angle A.
(iii) cos A is the abbreviation used for the cosecant of angle A.
(iv) cot A is the product of cot and A.
(v) sin θ = 43 for some angle.
Solution:

Jbc 2022* CLASS10 MATHS TRIGONOMETRY