Question

Prove that
1-tan ^4x \sec x= 1- tan​

Answer 1

Answer: the LHS

Step-by-step explanation:We will use the Identity  

:

sec

2

x

=

1

+

tan

2

x

.

The R.H.S.

=

2

sec

2

θ

−

sec

4

θ

=

sec

2

θ

(

2

−

sec

2

θ

)

=

(

1

+

tan

2

θ

)

{

1

+

(

1

−

sec

2

θ

)

}

=

(

1

+

tan

2

θ

)

{

1

−

(

sec

2

θ

−

1

)

}

=

(

1

+

tan

2

θ

)

(

1

−

tan

2

θ

)

=

1

2

−

(

tan

2

θ

)

2

=

1

−

tan

4

θ

=The L.H.S.