Question

what is the value of cosec²18⁰ - 1/cot²72⁰ ​

Answer 1

Answer:

cosec²18⁰-tan²72⁰

=cosec²(90-72)-tan²72⁰

=sec²72⁰-tan²72⁰

=1(by property - sec²x-tan²x=1)

Answer 2

cosec² 18° -

1

cot²72°

= cosec² 10° - tan² 72°

[∵ tan θ . cot θ = 1]

= cosec²18° – tan²(90° – 18°)

= cosec² 18° – cot² 18° = 1

[∵ tan (90° – θ = cot θ ; cosec² θ – cot² θ = 1]