Question

PROVE THAT ROOT 3 COS 23-SIN 23=2 COS 53

Answer 1

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Answer 2

$\sqrt{3}\cos23^\circ-\sin23^\circ =2\cos53^\circ$ Proved.

Step-by-step explanation:

Consider the provided information.

We need to prove that: $\sqrt{3}\cos23^\circ-\sin23^\circ =2\cos53^\circ$

Consider the Right hand side:

$2\cos53^\circ=2\cos(30^\circ+23^\circ)$

Use the property: $\cos(x+y)=\cos x \cos y-\sin x\sin y$

$2\cos53^\circ=2[\cos30^\circ\cos23^\circ-\sin30^\circ\sin23^\circ]$

$2\cos53^\circ=2[\frac{\sqrt{3}}{2}\cos23^\circ-\frac{1}{2}\sin23^\circ]$

$2\cos53^\circ=\sqrt{3}\cos23^\circ-\sin23^\circ$

LHS=RHS

Hence, proved

#Learn more

Prove the trigonometric identity 1+ cot square A= cosec square A

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