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If y = sin x^(@) " and " u = cos x " th...

If ` y = sin x^(@) " and " u = cos x " then " (dy)/(dx)` is equal to

A

`- "cosec x" * cos x `

B

`(pi)/(180)" cosec" x^(@) cos x `

C

` -(pi)/(180)" cosec" x^(@) cos x `

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
C
Since , ` y = sin x^(@) = sin"" ((pi x)/(180)) "" [ x^(@) = (pi x)/(180)]`
` therefore (dy)/(dx) = (pi)/(180) cos ""(pix)/(180) = (pi)/(180) cos x^(@)`
and ` u = cos x `
` therefore (du)/(dx) = - sin x `
Now , `(dy)/(dx) = ((dy)/(dx) )/((du)/(dx) ) = - ((pi)/(180) "" cos x^(@))/(sin x ) = - (pi)/(180) cos x^(@) " cosec " x `.
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