# Simplify cot^{2}θ(1 + tan^{2}θ)

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.

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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, sin^{2}x – 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 cot^{2}θ(1 + tan^{2}θ)

**Solution:**

cot

^{2}θ(1 + tan^{2}θ)(1 + tan

^{2}θ) = sec^{2}θSubstituting the value of 1 + tan

^{2}θ in the above expression,= cot

^{2}θ × (sec^{2}θ)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