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# Simplify cot2θ(1 + tan2θ)

• Last Updated : 03 Sep, 2021

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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