Question

Pls answer this
-(secx+tanx)(secx-tanx) = ?

Answer 1

Answer:

-1

Step-by-step explanation:

Using (a+b) (a-b) identity

-Sec²x + tan²x = - 1

Answer 2

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Let's start with the original:

(tanx+secx)(tanx−secx)

Let's now do FOIL:

(tanx)(tanx)=tan2x

(tanx)(−secx)=−tanxsecx

(secx)(tanx)=tanxsecx

(secx)(−secx)=−sec2x

Adding them all up:

tan2x−tanxsecx+tanxsecx−sec2x=tan2x−sec2x

There is a trig identity:

tan2x+1=sec2x

tan2x−sec2x=−1

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So we can finish up our simplification:

tan2x−tanxsecx+tanxsecx−sec2x=tan2x−sec2x=−1