If sec theta + tan theta =5, then.
sec theta - tan theta=
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If sec theta + tan theta =5, then.
sec theta - tan theta=
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[tex]\underline{\textbf{Given:}}[/tex]
[tex]\mathsf{sec\theta+tan\theta=5}[/tex]
[tex]\underline{\textbf{To find:}}[/tex]
[tex]\textsf{The value of}[/tex]
[tex]\mathsf{sec\theta-tan\theta}[/tex]
[tex]\underline{\textbf{Solution:}}[/tex]
[tex]\underline{\textbf{Identity used:}}[/tex]
[tex]\mathsf{sec^2A-tan^2A=1}[/tex]
[tex]\textsf{Using the above identity,}[/tex]
[tex]\mathsf{sec^2\theta-tan^2\theta=1}[/tex]
[tex]\mathsf{(sec\theta)^2-(tan\theta)^2=1}[/tex]
[tex]\textsf{Using the identity}\;\boxed{\mathsf{a^2-b^2=(a-b)(a+b)}}[/tex]
[tex]\mathsf{we\;get}[/tex]
[tex]\mathsf{(sec\theta-tan\theta)(sec\theta+tan\theta)=1}[/tex]
[tex]\mathsf{(sec\theta-tan\theta)(5)=1}[/tex]
[tex]\implies\boxed{\mathsf{sec\theta-tan\theta=\dfrac{1}{5}}}[/tex]