## Trigonometry Formulas, Tricks & Questions

Trigonometry is an important part of the Quantitative Aptitude section that gives a tough time to students with its complex formulas and questions. Trigonometry is a major branch of mathematics that deals with the angles and lengths of a right-angled triangle. The application of trigonometry is done in astronomical studies and other science fields. 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 the Trigonometry formulas, tricks, and questions in trigonometry revolve around these 6 functions. Aspirants can check out the details of Trigonometry including the formulas, tricks, and questions.

Cbsesolutions provide you with each and every formula related to trigonometry as well as tricks that will help you score well in your examinations and any other competitive exam like SSC, jee, etc.

**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**

**Important Results for Trigonometry**

- 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,

**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 +∞

**Trigonometry Formulas | Values of Trigonometric Ratios**

**Values of Trigonometric Functions**

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