Question

(1+cot square thita) (1-cos square thita) (1+cos square thita)=?​

Answer 1

Step-by-step explanation: We are given to simplify the following trigonometric expression :

E=(1-\cos\theta)(1+\cos\theta)(1+\cot^2\theta).E=(1−cosθ)(1+cosθ)(1+cot

2

θ).

We will be using the following formulas :

\begin{lgathered}(i)~1-\cos^2\theta=\sin^2\theta,\\\\(ii)~\cot\theta=\dfrac{\cos\theta}{\sin\theta}\\\\(iii)~(a-b)(a+b)=a^2-b^2.\end{lgathered}

(i) 1−cos

2

θ=sin

2

θ,

(ii) cotθ=

sinθ

cosθ

(iii) (a−b)(a+b)=a

2

−b

2

.

The simplification of the given expression is as follows :

Answer 2

( 1 + cot² theetha ) ( 1 - cos² theetha ) ( 1 + cos² theetha ) = sin² theetha

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