Question

prove that

(sin∅^4-cos^4∅ = 1) cosec^2∅=2

Answer 1

sin⁴∅ - cos⁴∅ = 1

(sin²∅ - cos²∅ )( sin²∅+ cos²∅ ) = 1

we know that ,

sin²∅ + cos²∅ = 1
so,
(sin²∅ - cos²∅).1 = 1 form above eqn
sin²∅ - cos²∅ = 1

sin²∅ -(1-sin²∅ ) = 1

2sin²∅ = 2

sin²∅ = 1

so, 1/cosec²∅ = 1

cosec² ∅ = 1

here some typing mistake
I think questions is
sin⁴∅ - cos⁴∅ = 1
then ,prove that cosec²∅ = 1
plz mention clearly , what you want