This Trigonometry tip was contributed by Saurav, a HashLearn tutor from NIT Durgapur.

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 cosxThe values of these kind of identities is given as,

Minimum : - √(a^2 + b^2)

Maximum: + √(a^2 + b^2)

Minimum : - √(a^2 + b^2)

Maximum: + √(a^2 + b^2)

__Type 2__: (sinx cosx)^nThe values of these kind of identities is given as,

Minimum : (1/2)^n

Maximum: Value can go upto infinity

Minimum : (1/2)^n

Maximum: Value can go upto infinity

__Type 3__: a sin^2 x + b cos^2 xThe values of these kind of identities is given as follows:

(If a > b)

Minimum : b

Maximum: a

(If a < b)

Minimum : a

Maximum: b

(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 xThe values of these kind of identities is given as,

Minimum : 2√(ab)

Maximum: Value can go upto infinity

Minimum : 2√(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,

Then, according to the formula:

Maximum value for the expression is,

= √(4^2+3^2) + 5

= 5 + 5

= 10

Minimum value for the expression is,

= √(4^2+3^2) - 5

= 5 - 5

= 0

**4sinx + 3cosx + 5**, then you have to apply the**Type-1**formula.Then, according to the formula:

Maximum value for the expression is,

= √(4^2+3^2) + 5

= 5 + 5

= 10

Minimum value for the expression is,

= √(4^2+3^2) - 5

= 5 - 5

= 0

Found it useful? Tag your friends in the comments or

**share this post on Facebook**.