Prove that:

Question

(tan²Θ)x(sin²Θ) = (tan²Θ)-(sin²Θ)

show work

Answer 1

LS = (sin^2 Ø)/cos^2 Ø) * sin^2 Ø
= sin^4 Ø/cos^2 Ø

RS = sin^2 Ø / cos^2 Ø - sin^2 Ø
= (sin^2 Ø - sin^2 Ø(cos^2 Ø) )/cos^2 Ø
= sin^2 Ø( 1 - cos^2 Ø)/cos^2 Ø
= sin^2 Ø (sin^2 Ø) /cos^ Ø
= sin^4 Ø / cos^2 Ø
= LS

Answer 2

Thank You!!!

Answer 3

True/False.
sec Θ ° > tan Θ ° for every angle Θ.

Please explain why?