Question

Prove:
a) Cos x . tg x . cossec x = 1
b) Tg x . cos x = sen x
c) (1 + sen x) (1 - sen x) = cos²x
d) tg²x . cossec²x = 1 + tg²x

Answer 1

a)cos x .tg x .cossec x

cos x . $\frac{sen x}{cos x} .\frac{1}{sen x}$

$\frac{cos x . sen x}{cos x . sen x}$

1

b) tg x . cos x

$\frac{sen x}{cos x} .cos x$

sen x

c)(1 + sen x)(1 - sen x)

1 - $sen^{2}x$

$cos^{2} x$

d)$tg^{2} x.cossec^{2}x$

$\frac{sen^{2}x}{cos^{2}x} . \frac{1}{cos^{2}x}$

$\frac{1}{cos^{2}x}$

$\frac{sen^{2}x+cos^{2}x}{cos^{2}x}$

$\frac{cos^{2}x}{cos^{2}x}+\frac{sen^{2}x}{cos^{2}x}$

1 + $tg^{2} x$