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  • (tanθ + 2) (2 tan θ + 1) = 5 tan θ + sec power 2 θ.

(tanθ + 2) (2 tan θ + 1) = 5 tan θ + sec2θ.

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 (tanθ + 2) (2 tan θ + 1) = 5 tan θ + sec2θ
Taking L.H.S.
(tanθ + 2) (2 tan θ + 1) 
tanθ.(2tan θ+1) + 2(2tan θ +1)
2\tan ^{2}\theta +\tan \theta +4\tan \theta+2
2\tan ^{2}\theta +5\tan \theta+2
2\left ( \tan ^{2}\theta +1 \right )+5\tan \theta\: \cdots \left ( 1 \right )
We know that

\sec ^{2 }\theta-\tan ^{2}\theta= 1
\left ( 1+\tan ^{2}\theta= \sec ^{2}\theta \right )  

Put the above value in (1)we get
2\sec ^{2}\theta +5\tan \theta \neq 5\tan \theta +\sec ^{2}\theta
L.H.S. \neq R.H.S.
Hence the given expression is false.

 

 

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infoexpert27

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