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Basic Trigonometric Identities

State true1 o...

Question

State true(1) or false(0):
$(tan θ + 2) (2 tan θ + 1) = 5 tan θ + s e c^{2} θ$

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Solution

LHS $= 2 {tan}^{2} θ + tan θ + 4 tan θ + 2 = 2 {tan}^{2} θ + 5 tan θ + 2$
$= 2 {sec}^{2} θ - 2 + 5 tan θ + 2$
$= 2 {sec}^{2} θ + 5 tan θ$
$\neq$ RHS

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