Question

Tantheta in terms of sectheta

Answer 1

Answer:

The required expression is \tan\theta=\sqrt{1-\sec^2\theta}tanθ=

1−sec

2

θ

Step-by-step explanation:

To express : \tan\thetatanθ in terms of \sec\thetasecθ ?

Solution :

Using trigonometric identities,

\sec^2\theta-\tan^2\theta=1sec

2

θ−tan

2

θ=1

Arrange, \tan\thetatanθ in terms of \sec\thetasecθ

\tan^2\theta=1-\sec^2\thetatan

2

θ=1−sec

2

θ

Taking root both side,

\sqrt{\tan^2\theta}=\sqrt{1-\sec^2\theta}

tan

2

θ

=

1−sec

2

θ

\tan\theta=\sqrt{1-\sec^2\theta}tanθ=

1−sec

2

θ

Therefore, The required expression is \tan\theta=\sqrt{1-\sec^2\theta}tanθ=

1−sec

2

θ

Answer 2

Answer:

${ \tan( \alpha ) }^{2} = 1 + { \sec(\alpha )}^{2}$