Table of Content

• What is Trigonometry Ratio?
• Trigonometric Ratio Formulas Class 10
• All Trigonometry Formulas Class 10
• Trigonometric Reciprocal Identities
• Trigonometric Identities
• Complementary Angle Formulas
• Supplementary Angle Formulas
• Even and Odd Angle Formulas
• Double Angle Formulas
• Solved Examples on Trigonometry Formulas Class 10
• Practice Questions on Trigonometric Formulas Class 10

θ	0°	30°	45°	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	Not defined
cosec θ	Not defined	2	√2	2/√3	1
sec θ	1	2/√3	√2	2	Not defined
cot θ	Not defined	√3	1	1/√3	0

All Trigonometry Formulas Class 10

List of all Trigonometric Formulas essential for Class 10 is mentioned below:

Trigonometric Reciprocal Identities

Reciprocal Identities in trigonometry are:

• sin θ = 1/cosec θ ⇒ cosec θ = 1/sin θ
• cos θ = 1/sec θ ⇒ sec θ = 1/cos θ
• tan θ = 1/cot θ ⇒ cot θ = 1/tan θ

Pythagorean Identities

Pythagorean Identities in trigonometry are:

• sin²θ + cos²θ = 1
• 1 + tan²θ = sec²θ
• 1 + cot²θ = cosec²θ

Complementary Angle Formulas

Trigonometry ratios of complementary angles are:

• sin(90 – θ) = cos θ
• cos(90 – θ) = sin θ
• tan(90 – θ) = cot θ
• cot(90 – θ) = tan θ
• sec(90 – θ) = cosec θ
• cosec(90 – θ) = sec θ

Supplementary Angle Formulas

• sin(180 – θ) = sin θ
• cos(180 – θ) = -cos θ
• tan(180 – θ) = -tan θ
• cot(180 – θ) = -cot θ
• sec(180 – θ) = -secθ
• cosec(180 – θ) = cosec θ

Even and Odd Angle Formulas

• sin(-θ) = -sin θ
• cos(-θ) = cos θ
• tan(-θ) = -tan θ
• cot(-θ) = -cot θ
• sec(-θ) = sec θ
• cosec(-θ) = -cosec θ

Double Angle Formulas

Double angle formulas are:

• sin 2θ = 2sinθ.cosθ
• cos 2θ = 1 – 2sin²θ
• tan 2θ = 2tanθ/(1-tan²θ)

Also, Check

• Trigonometry
• Trigonometric Formulas
• Trigonometric Identities
• Trigonometric Identities Class 10
• Sin 30 Degrees
• Height and Distance

Solved Examples on Trigonometry Formulas Class 10

Example 1: If sin A = 3/4. Calculate cos A and tan A

Solution:

cos²A = 1 – sin²A

⇒ cos²A = 1-(9/16)

⇒ cos²A = 7/16

⇒ cosA = √7/4

⇒ tanA = sinA/cosA

⇒ tanA = 3/√7

Example 2: Given 15 cot A = 8. Find sin A and sec A

Solution:

cotA = 8/15

⇒ cosec²A = 1 + cot²A

⇒ cosec²A = 1 + (64/225)

⇒ cosec²A = 289/225

⇒ cosecA = 17/15

⇒ sinA = 15/17

⇒ secA = cosecA/cotA

⇒ secA = 17/8

Example 3: Find the value of sin 45° – cos 45°.

Solution:

sin 45° = cos 45° = 1/√(2)

⇒ sin 45° – cos 45° = 0

Example 4: If tan θ + cot θ = 7. Find tan²θ + cot²θ

Solution:

tan θ + cot θ = 7

⇒ (tanθ + cotθ)² = 49

⇒ tan²θ + cot²θ + 2tanθcotθ = 49

⇒ tan²θ + cot²θ + 2 = 49

⇒ tan²θ + cot²θ = 47

Example 5: The value of tan θ = 3/4. Find the value of sec θ.

Solution:

1 + tan²θ = sec²θ

⇒ 1 +(3/4)² = sec²θ

⇒ sec²θ = 25/16

⇒ secθ = 5/4

Example 6: If sec θ + tan θ = 5. Find sec θ – tan θ.

Solution:

sec 2θ – tan 2θ = 1

⇒ (sec θ + tan θ)(sec θ – tan θ) = 1

⇒ 5(sec θ – tan θ) = 1

⇒ sec θ – tan θ = 1/5

Practice Questions on Trigonometric Formulas Class 10

1. Prove that (cos θ/(1 – tan θ)) + (sin θ/(1 – cot θ)) = sin θ + cos θ.

2. Prove that tan²θ + cot²θ +2 = sec²θ * cosec²θ.

3. If cosec θ + cot θ = 9. find cos θ.

4. If cos θ = 4/5. Find all other trigonometric ratios.

5. Find the value of sin 60° cos 30° + cos 30° sin 60°.

6. Find the value of tan 30°/cot 60°.

7. Find the value of (sin 30° + cos 30°) – (sin 60° + cos 60°).

8. If tanθ + cotθ = 1. Find the value of tan¹⁰θ + cot¹⁰θ.

9. Find the value of sin 45° + cos 45°.

10. Find the value of cos 19°/sin 71°.

Trigonometry Formula Class 10 – FAQs

What are Trigonometric Ratio Formulas in Class 10.

Trigonometric Ratio Formulas establish the relation between Trigonometric Ratios and the sides of a right triangle.

What is Reciprocal of tan θ?

cot θ = 1/tanθ

What is the value of sin(-θ)?

sin(-θ) = -sinθ

What is the relation between cot θ and cosec θ?

1 + cot²θ = cosec²θ

How is tan θ related to sin θ and cos θ?

tan θ = sin θ/cos θ

What is the value of sin 30?

sin 30 = 1/2

How is cosecθ related to sinθ?

cosecθ = 1/sinθ

What is the value of tan 45?

tan 45 = 1

What is the value of Cos(-θ)?

cos(-θ) = cosθ

Is Trigonoimetry Formula Class 10 important?

Yes, Trigonometry Formula Class 10 is very important for Class 10 students as they can always expect questions from this in their exams.