Answer:
[tex]\sin \left(90^{\circ \:}-x\right)=\cos \left(x\right)[/tex]
Hence, option D is correct.
Step-by-step explanation:
Given the expression
[tex]sin\:\left(90^{\circ }\:-\:x\right)[/tex]
Using the angle difference identity
[tex]\sin \left(s-t\right)=\sin \left(s\right)\cos \left(t\right)-\cos \left(s\right)\sin \left(t\right)[/tex]
so the expression becomes
[tex]sin\:\left(90^{\circ }\:-\:x\right)=\sin \:\left(90^{\circ \:\:}\right)\cos \:\left(x\right)-\cos \:\left(90^{\circ \:\:}\right)\sin \:\left(x\right)[/tex]
as sin 90° = 1
so sin 90° cos x = cos x
also
cos 90° = 0
so con (90°) sin x = 0
Thus, the expression becomes
[tex]\sin \:\left(90^{\circ \:\:}\right)\cos \:\left(x\right)-\cos \:\left(90^{\circ \:\:}\right)\sin \:\left(x\right)=\cos \:\left(x\right)-0[/tex]
[tex]= cos (x)[/tex] ∵ [tex]\cos \left(x\right)-0=\cos \left(x\right)[/tex]
Therefore,
[tex]\sin \left(90^{\circ \:}-x\right)=\cos \left(x\right)[/tex]
Hence, option D is correct.
