Question

Prove the identity step by step cosx /1+sinx=secx-tanx

Answer 1

Step-by-step explanation:

We have,

cos

x

1

−

sin

x

,

=

cos

x

1

−

sin

x

×

1

,

=

cos

x

1

−

sin

x

×

1

+

sin

x

1

+

sin

x

,

=

cos

x

(

1

+

sin

x

)

1

−

sin

2

x

,

=

cos

x

(

1

+

sin

x

)

cos

2

x

,

=

1

+

sin

x

cos

x

,

=

1

cos

x

+

sin

x

cos

x

,

=

sec

x

+

tan

x

, as desired!

thanks you