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# Trigonometry Formula, Tricks, Identities, Trigonometric Ratio

## Trigonometry

Trigonometry Formula: Trigonometry is an important part of the Quantitative Aptitude section that gives a tough time to students with its complex formula trigonometry and questions. Trigonometry is a major branch of mathematics that deals with the angles and lengths of a right-angled triangle. The application of all formula trigonometry is done in astronomical studies and other science fields.

## Trigonometry Formulas

There are a total of 6 trigonometric functions namely Sin, Cos, Tan, Sec, Cosec, and Cot. There are trigonometric ratios that help to derive the current length and angle. All Trigonometry formulas, trigonometry formulas tricks, and questions in trigonometry revolve around these 6 functions. Aspirants can check out the details of Trigonometry including the formulas, trigonometry formulas tricks, and questions.

Questions on the Trigonometry topic are asked in various competitive examinations such as SSC, Railway, etc. In this post, we are providing you with the Formula Trigonometry notes useful for the examinations. It will help you memorize the basic formulas Trigonometry. Here are the all trigonometry formulas for class 10 and trigonometry formulas for class 11th which can be helpful for the preparation in the 10th and 12th classes as well.

## Important Trigonometric Ratio Identities

In order to get hold of the basic concepts of trigonometry, you must learn all the important trigonometric ratio and their identities.

Trigonometric Ratios

To study different trigonometric ratio functions,  we will use a right-angled triangle. Suppose ABC is a right-angled triangle with angle A = 90°

Relations between Trigonometric Ratios

Value of Trigonometric Ratios in Different Quadrants

Different Values of Specific Angle of Trigonometric Ratio

You must learn the following table to solve the question based on the trigonometrical ratio of angle 0°, 30°, 45°, 60°

Trigonometry Formula: Relation Between Square Of Different Types Of Trigonometric ratios

Important Concept to Solve a Specific Type of Question

If A + B = 90°

Results that are true always :

(i)  sin A. sec B = 1 or  sin A = cos B

(ii) cos A. cosec B = 1 or  sec A = cosec B

(iii) tan A. tan B = 1  or tan A = cot B

(iv) cot A. cot B = 1

(v)  sin²A + sin² B = 1

(vi) cos² A + cos² B = 1

Important Trigonometry Formula for Sum and Difference Of Two Angles

(1) sin (A+B) =sinA. cosB + cosA sinB

(2) sin(A – B) =sinA. cosB – cosA sinB

(3) cos(A+B) =cosA. cosB – sinA sinB

(4) cos(A-B) = cosA. cosB+sinA sinB

(5) 2 sinA.cosB = sin(A+B)+sin (A-B)

(6) 2 cosA. sinB = sin(A+B)-sin (A-B)

(7) 2 sinA. sinB = cos(A-B)-cos(A+B)

(8) 2 cosA.cosB = cos(A+B)+cos(A-B)

(9) sin²A-sin²B = sin(A+B). sin(A-B)

(10) cos²A-cos²B = cos(A+B).cos (A-B)

Trigonometry Formulas For Tangent

### Trigonometry Formulas List

• If A + B + C = 180°

Then, tan A + tan B + tan C = tan A. tan B. tan C

• If A + B + C = 90°

Then,  cot A + cot B + cot C = cot A cot B cot C

• If (a) sin θ + cosec θ = 2

Then,

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### Trigonometry Maximum & Minimum Value

Maximum & Minimum Value

Minimum                           Maximum

• sin θ, cos θ [odd power]             –1                                         +1
• sin θ, cos θ [even power]             0                                         +1
• tan θ, cot θ [odd power]             –∞                                       +∞
• tan θ, cot θ [even power]             0                                        +∞
• sec θ, cosec θ [odd power]         –∞                                       +∞
• sec θ, cosec θ [even power]        +1                                        +∞

## FAQs

### Q. What is the formula of sin (A+B)?

Ans. The formula of sin (A+B) is sinA. cosB + cosA sinB

### Q. In which quadrant, all the Trignometric values are positive?

Ans In the 1st quadrant all the Trignometric values are positive

#### Congratulations!

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