Aishaalme7idn
Answered

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(secx-tanx)(secx+tanx)=1 simplify

Sagot :

Nischalrijalidn

Step-by-step explanation:

(secx-tanx)(secx+tanx)

=sec^2-tan^2

=1

Devishri1977idn

Answer:

Step-by-step explanation:

LHS = (sec x - tan x)(Sec x - tan x)    

      = sec² x - tan²x         {(a +b)(a-b) = a² - b²}

      [tex]= \dfrac{1}{Cos^{2} \ x}-\dfrac{Sin^{2} \ x}{Cos^{2} \ x}\\\\\\= \dfrac{1-Sin^{2} \ x}{Cos^{2} \ x}\\\\= \dfrac{Cos^{2} \ x}{Cos^{2} \x}\\\\= 1[/tex]

Hence proved.

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