it is given 3cosec ϴ=4, then verify that cosec^2ϴ-cot^2ϴ=1
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3cosec ϴ=4
cosec ϴ=4/3
squaring both sides
cosec^2ϴ=16/9
we know that
cosec^2ϴ-cot^2ϴ=1
16/9-cot^2ϴ=1
-cot^2ϴ=1-16/9
-cot^2ϴ=-7/9
cot^2ϴ=7/9
L.H.S,
=cosec^2ϴ-cot^2ϴ
=16/9-7/9
=(16-7)/9
=9/9
=1 proved
cosec ϴ=4/3
squaring both sides
cosec^2ϴ=16/9
we know that
cosec^2ϴ-cot^2ϴ=1
16/9-cot^2ϴ=1
-cot^2ϴ=1-16/9
-cot^2ϴ=-7/9
cot^2ϴ=7/9
L.H.S,
=cosec^2ϴ-cot^2ϴ
=16/9-7/9
=(16-7)/9
=9/9
=1 proved
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