Question

Доказать тождество
tg²L - sin²L = tg²L·Sin²L

Answer 1

$tg^2L-sin^2L=\frac{sin^2L}{cos^2L} -sin^2L=\frac{sin^2L-sin^2L*cos^2L}{cos^2L} =\\ \\ \frac{sin^2L(1-cos^2L)}{cos^2L} =\frac{sin^2L*sin^2L}{cos^2L} =tg^2L*sin^2L$

Answer 2

tg
2
L−sin
2
L=
cos
2
L
sin
2
L
​
−sin
2
L=
cos
2
L
sin
2
L−sin
2
L•cos
2
L
​
=
cos
2
L
sin
2
L(1−cos
2
L)
​
=
cos
2
L
sin
2
L•sin
2
L
​
=tg
2
L•sin
2
L
​