1.

Prove that: i. (sin2 θ / cos θ) + cos θ = sec θii. cos2 θ (1+ tan2 θ) = 1

Answer»

i. L.H.S = (sin2 θ/cos θ) + cos θ 

= (sin2 θ/cos2 θ)/cos θ 

= 1/cos θ  ....[∵ sin2 θ + cos2 θ = 1]

= sec θ

= R.H.S

∵ (sin2 θ/cos θ) + cos θ = sec θ

ii. L.H.S. = cos2 θ (1 + tan2 θ) 

= cos2 θ sec2 θ …[∵ 1 + tan2 θ = sec2 θ]

= cos2 θ . 1/cos2 θ  ....[∴ sec θ = 1/cos θ]

= 1

= R.H.S

∴ cos2 θ (1 + tan2 θ) = 1



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