Question

if ( sec A - tan A) = x then prove that
$\frac{1 + { \times }^{2} }{1 - { \times }^{2} } = cosec \: a$
​

Answer 1

Answer:

Answer

1+secA

tanA

−

1−secA

tanA

=2⋅cosecA

L.H.S

1+secA

tanA

−

1−secA

tanA

=

1−sec

2

A

tanA(1−secA)−tanA(1+secA)

=

−tan

2

A

tanA(1−secA−1−secA)

=

−tanA

−2secA

=

sinA/cosA

2⋅1/cosA

=

sinA

2

=2⋅cosecA

=R.H.S

∴ L.H.S=R.H.S.