Prove that (tanθ + 2) (2 tanθ + 1) = 5 tanθ + 2sec2
θ.
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Step-by-step explanation:
(tanθ+cotθ)
2
=sec
2
θ+cosec
2
θ
L.H.S (tanθ+cotθ)
2
=tan
2
θ+cot
2
θ+2tanθcotθ
=sec
2
θ−1+cosec
2
θ−1+2tanθ
tanθ
1
=sec
2
θ+cosec
2
θ−2+2
=sec
2
θ+cosec
2
θ
=R.H.S.
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