Question

3 cosec ø = 4, find cosec²ø - cot²ø​

Answer 1

3cosecA=4

=>cosecA=4/3

=>sinA=3/4

so,cos^2A=7/16

so,cosec^2A-cot^2A=16/9 -7/16

=193/144

Answer 2

$3 \: cosec \: θ = 4 \\ cosec \: θ = \frac{4}{3} \\ cot {}^{2}θ = cosec {}^{2}θ - 1$

${cot}^{2} θ = (\frac{4}{3} ) {}^{2} - 1 \\ = \frac{16}{9} - 1 = \frac{16 - 9}{9} = \frac{7}{9}$

$cosec {}^{2} θ - {cot}^{2} θ = \frac{16 - 7}{9} = \frac{9}{9} = 1$