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If sin[pi/4.cottheta]=cos[pi/4tantheta],...

If `sin[pi/4.cottheta]=cos[pi/4tantheta]`, then `theta` =

A

`2npi+(pi)/(4)`

B

`2npi+-(pi)/(4)`

C

`2npi-(pi)/(4)`

D

`npi+(pi)/(4)`

Text Solution

Verified by Experts

The correct Answer is:
D
Given , `sin((pi)/(4) "cot"theta)=cos((pi)/(4) "tan"theta)`
`rArrsin((pi)/(4) "cot"theta)=sin((pi)/(2)-(pi)/(4)"tantheta)`
`rArr(pi)/(4)(tantheta+cottheta)=(pi)/(2)rArrtantheta+cottheta-2=0`
`rArrtan^(2)theta-2tantheta+1=0rArr(tantheta-1)^(2)=0`
`rArrtantheta=1="tan"(pi)/(4)`
`thereforetheta=npi+(pi)/(4)`
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