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## 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.

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