1.

Write ‘True’ or ‘False’ and justify your answer.(tan θ + 2) (2 tan θ + 1) = 5 tan θ + sec2 θ.

Answer»

False

Justification:

L.H.S = (tan θ+2) (2 tan θ+1)

= 2 tan2 θ + tan θ + 4 tan θ + 2

= 2 tan2θ+5 tan θ+2

Since, sec2 θ – tan2 θ = 1, we get, tan2θ = sec2 θ-1

= 2(sec2 θ-1) +5 tan θ+2

= 2 sec2 θ-2+5 tan θ+2

= 5 tan θ+ 2 sec2 θ ≠R.H.S

∴, L.H.S ≠ R.H.S



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