Let us show that:

cosec²48° - tan²42° = 1

Given, cosec² 48° - tan² 42°

Need to prove the given equation as one

⇒ we know that tan(90 - θ) = cotθ

∴ tan42° = tan(90 - 48)°

= cot48° - - - eq (1)

⇒ Substitute eq(1) in the given equation

∴ cosec² 48° - cot²48°

⇒ we know that

And

∴

=

[ sin²θ + cos²θ = 1

∴ 1 - cos²θ = sin²θ]

⇒

= 1

∴ cosec² 48° - tan² 42° = 1

Hence, proved