# Simplify cot2θ(1 + tan2θ)

The word trigonon means triangle and metron meaning measure. So, trigonometry is the branch of mathematics that deals with the sides and angles of a triangle where one of the angles is 90°. Trigonometry finds its applications in various fields such as engineering, image compression, satellite navigation, and architecture.

Trigonometric function, also known as angle function or circular function, is a function of an angle or arc. It is simply expressed in terms of the ratios of pairs of sides of a right-angled triangle. The six commonly used trigonometric functions are: sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), cosecant (cosec) angles.

Where P is the perpendicular, B is the base, and H is the hypotenuse.

A trigonometric equation is an equation involving one or more trigonometric ratios of unknown angles. For example, sin2x – 5 cosx = 1/2.

### Trigonometric Identities

Trigonometric identities are equations involving trigonometric functions that hold for all possible values of the variables. In trigonometry, there are a variety of identities that are used to solve a variety of trigonometric problems. They are as follows,

Pythagorean Trigonometric Identities

Reciprocal Trigonometric Identities

Co-function Identities

Complementary Angle Identities

Supplementary Angle Identities

### Simplify cot2θ(1 + tan2θ)

Solution:

cot2θ(1 + tan2θ)

(1 + tan2θ) = sec2θ

Substituting the value of 1 + tan2θ in the above expression,

= cot2θ × (sec2θ)

Recognize that,  and

On substituting the value of cotθ and secθ in the above expression,

### Sample Questions

Question 1: Find the value of

Solution:

Substituting the value of  in the above expression,

Question 2: Find the value of

Solution:

therefore,

Question 3: Find the value of

Solution:

Also,   and

=

Question 4:  Find the value of

Solution:

, therefore,

Also, we are aware that

=1

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