It's trigo time #6

Geometry Level 2

Simplify the following expression:

csc ⁡ β sin ⁡ β − cot ⁡ β tan ⁡ β \large \frac {\csc \beta}{\sin \beta} - \frac {\cot \beta}{\tan \beta}

This is a part of the set: It's trigo time

0 sin ⁡ 2 β \sin^2\beta tan ⁡ 2 β \tan^2\beta -1 sin ⁡ β \sin\beta cos ⁡ 2 β \cos^2\beta 1

Syed Hamza Khalid by Syed Hamza Khalid , 17, France

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2 solutions

Syed Hamza Khalid
May 13, 2017

7 Helpful 0 Interesting 0 Brilliant 0 Confused

You are amazing!

gaindu poorna - 4 years ago
Munem Shahriar
Feb 27, 2018

csc ⁡ β sin ⁡ β − cot ⁡ β tan ⁡ β = csc ⁡ β 1 csc ⁡ β − cot ⁡ β 1 cot ⁡ β = csc ⁡ 2 β − cot ⁡ 2 β = 1 \begin{aligned} \dfrac{\csc \beta}{\sin \beta} - \dfrac{\cot \beta}{\tan \beta} & = \dfrac{\csc \beta}{\frac 1{\csc \beta}} - \dfrac{\cot \beta}{\frac 1{\cot \beta}} \\ & = \csc^2 \beta - \cot^2 \beta\\ & = \boxed1 \\ \end{aligned}

1 Helpful 0 Interesting 0 Brilliant 0 Confused

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