# Study Tips: Finding Values For Trigonometric Identities

With this tip, you will learn:

The 4 types of trigonometric identities

The formulae to find maximum & minimum values for trigonometric identities for each type

- An example problem to solve

**What are the different types of trigonometric identities?**

#### Type 1: a sinx±b cosx ; a sinx±b sinx ; a cosx±b cosx

The values of these kind of identities is given as,

Minimum : - sqrt(a^2 + b^2)

Maximum: + sqrt(a^2 + b^2)

#### Type 2: (sinx cosx)^n

The values of these kind of identities is given as,

Minimum : (1/2)^n

Maximum: Value can go upto infinity

#### Type 3: a sin^2 x + b cos^2 x

The values of these kind of identities is given as follows:

(If a > b)
Minimum : b

Maximum: a

(If a < b)
Minimum : a

Maximum: b

#### Type 4: a sin^2 x + b cosec^2 x ; a cos^2 x + b sec^2 x ; a tan^2 x ± b cot^2 x

The values of these kind of identities is given as,

Minimum : 2.sqrt(ab)

Maximum: Value can go upto infinity

**Note :** These formulae can only be applied once the expression has been deduced to appear like any one of the above types.

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Need help with problems in Trigonometry from tutors like Saurav? Download the HashLearn app & get instant help.

#### How can I solve problems where a constant C is present?

For example, if you are asked to find out the maximum and minimum values for the expression, **4sinx + 3cosx + 5**, then you have to apply the **Type-1** formula.

Then, according to the formula:

Maximum value for the expression is,

= sqrt(4^2+3^2) + 5

= 5 + 5

= 10

Minimum value for the expression is,

= sqrt(4^2+3^2) - 5

= 5 - 5

= 0

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