यदि 0 2 x ¬ S और secx = cosecy, तो sin (x+y) का मूल्य है :

secx = cosecy ⇒ cosx = siny $Rightarrow sin left(frac{pi}{2}-x ight)=sin y$ $Rightarrow y=frac{pi}{2}-x Rightarrow x+y=frac{pi}{2}$ $herefore sin (x+y)=sin frac{pi}{2}=1$

Alternative:

Let

x = y = 45°

∴ sec x = cosec y

sec 45° = cosec 45° = 2

sin (x + y) = sin (45° + 45°)

= sin 90° = 1