Question

express cos theta in terms of cosec theta

Answer 1

$cos \theta = {\sqrt{cosec^{2} \theta -1} /cosec \theta$

Answer 2

cosθ in terms of cosecθ is ( $\sqrt{cosecθ-1}$ / cosecθ)

Given:

cosθ

To Find:

cosθ in terms of cosecθ

Solution:

tanθ = sinθ / cosθ

Therefore,

cosθ = sinθ / tanθ

= sinθ cotθ

= sinθ ($\sqrt{cosec^2θ - 1}$)

=( $\sqrt{cosec^2θ-1}$) sinθ

= ( $\sqrt{cosec^2θ-1}$) / cosecθ

( Here the symbol capital I and θ are the same)

Hence, cosθ in terms of cosecθ is ( $\sqrt{cosecθ-1}$ / cosecθ)

#SPJ2