If x + y = 90°, then what is √(cos x cosec y - cos x sin y ) equal to

Question

If \(x\) + y = 90°, then what is \(\sqrt{\text{cos}\,x\,cosec\,y\,-\,cos\,x\,sin\,y}\) equal to 

(a) cos \(x\) 

(b) sin \(x\) 

(c) \(\sqrt{cos\,x}\)

(d) \(\sqrt{sin\,x}\)

Answer 1

(b) sin x

\(x\) + y = 90° ⇒ y = 90° – \(x\)

∴ \(\sqrt{\text{cos}\,x\,cosec\,y\,-\,cos\,x\,sin\,y}\)

= \(\sqrt{cox\,x\,cosec\,(90°-x)-cox\,x\,sin(90°-x)}\)

= \(\sqrt{cos\,x\,sec\,x\,-cos\,x\,cos\,x}\)

= \(\sqrt{1-cos^2\,x}=\sqrt{sin^2\,x}=sin\,x\)