Prove the identity sin thetacsc theta cos thetasec theta 1

Prove the identity: sin theta/csc theta + cos theta/sec theta = 1

Solution

(sin/csc) +(cos/sec)

write csc as 1/sin , sec as 1/cos

=(sin/(1/sin)) +(cos/(1/cos))

=sin² +cos²

sin=oppositeside/hypotenuse ,cos=adjacent side/hypotenuse

=(oppositeside/hypotenuse)²+(adjacent side/hypotenuse)²

=(oppositeside²+adjacent side²)/hypotenuse²

=hypotenuse²/hypotenuse²

=1

therefore (sin/csc) +(cos/sec)=1