Question

prove that cos x - cos 2x + cos 3x / sin x - sin 2x + sin 3x = cot 2x​

Answer 1

SOLUTION

TO PROVE

$\displaystyle \sf{ \frac{ \cos x - \cos 2x + \cos 3x}{\sin x - \sin 2x + \sin 3x} = \cot 2x }$

PROOF

LHS

$\displaystyle \sf{ = \frac{ \cos x+ \cos 3x - \cos 2x }{\sin x+ \sin 3x - \sin 2x } }$

$\displaystyle \sf{ = \frac{2 \cos \frac{x + 3x}{2} \cos \frac{x - 3x}{2} - \cos 2x }{2 \sin \frac{x + 3x}{2} \cos \frac{x - 3x}{2} - \sin 2x } }$

$\displaystyle \sf{ = \frac{2 \cos \frac{4x}{2} \cos \frac{- 2x}{2} - \cos 2x }{2 \sin \frac{4x }{2} \cos \frac{ - 2x}{2} - \sin 2x } }$

$\displaystyle \sf{ = \frac{2 \cos 2x \cos x - \cos 2x }{2 \sin 2x \cos x - \sin 2x } }$

$\displaystyle \sf{ = \frac{\cos 2x (2 \cos x - 1) }{ \sin 2x (2\cos x - 1) } }$

$\displaystyle \sf{ = \frac{\cos 2x }{ \sin 2x } }$

$\displaystyle \sf{ = \cot 2x }$

= RHS

Hence proved

━━━━━━━━━━━━━━━━

Learn more from Brainly :-

1. prove that (1+cos18)(1+cos54)(1+cos126)(1+cos162)=1÷16

https://brainly.in/question/29235086

2. Find the value of cot (-3155°)

https://brainly.in/question/6963315

Answer 2

Answer:

May it helps you...

Step-by-step explanation:

In this question only 4 formulas are used...

Firstly take LHS..

Then put the formulas in the question..

Then you find that your RHS be coming..

LHS =RHS

Hence proved

Thank you.