Question 6
Write ‘True’ or ‘False’ and justify your answer in each of the following:
$(t a n θ + 2) (2 t a n θ + 1) = 5 t a n θ + s e c^{2} θ$

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Solution

The statement is true.

LHS $= (t a n θ + 2) (2 t a n θ + 1)$

$= 2 t a n^{2} θ + 4 t a n θ + t a n θ + 2$

$= 2 (s e c^{2} θ - 1) + 5 tan θ + 2 ⌊ ∵ s e c^{2} θ - t a n^{2} θ = 1 ⌋$

$= 2 s e c^{2} θ + 5 t a n θ = R H S$

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