Question

if sec ∅ + tan ∅= m and sec ∅ - tan ∅ = n prove that mn = 1
pls prove
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Answer 1

Answer:

(secθ+tanθ)=m....(1) and

(secθ−tanθ)=n....(2)

Multiply (1) and (2), we have

⇒(secθ+tanθ)(secθ−tanθ)=mn

⇒(sec

2

θ−tan

2

θ)=mn

∴1=mn

Or mn=1

Hence proved

Answer 2

$\rm{m\times n\:is\:equal\:to\:(sec\:\theta+tan\:\theta)(sec\:\theta-tan\:\theta)}$

$\longrightarrow\rm{mn =(sec\:\theta+tan\:\theta)(sec\:\theta-tan\:\theta) }$

$\longrightarrow\rm{mn =sec^2\:\theta-tan^2\:\theta\quad...\:Since\:(a+b)(a-b)=a^2-b^2}$

$\longrightarrow\rm{mn =1/\cos ^{2} \theta-\sin ^{2} \theta/\cos ^{2} \theta\quad...\:Since\:sec\:\theta=1/\cos\theta\:\&\: tan\:\theta=\sin\:\theta/\cos\:\theta}$

$\longrightarrow\rm{mn =(1-\sin ^{2} \theta)/\cos ^{2} \theta=\cos ^{2} \theta/\cos ^{2} \theta}$

$\longrightarrow\rm{mn =1\quad...\:Hence\:Proved!}$