AM-2505

Proving identities

A Math · Secondary 4 · Medium · Proving identities

Prove the identity

(1+\tan x)(1-\tan x)=\cos2x

. Which of the following is the correct first step?

Write $(1+\tan x)(1-\tan x)=1-\tan^2x$ .
Replace $\tan x$ by $\dfrac1{\cos x}$ .
Replace $\cos2x$ by $1-2\sin^2x$ .
Divide both sides by $\sin x$ .

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