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If tan(picostheta)=cot(pisintheta), then...

If `tan(picostheta)=cot(pisintheta)`, then `cos(theta-(pi)/(4))=pm(1)/(2sqrt(2))`.

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we have, `tan(picostheta)=cot(pisintheta)`
`rArr" "tan(picostheta)=tan[(pi)/(2)-(pisintheta)]`
`rArr" "picos=(pi)/(2)-pisintheta`
`rArr" "pi(sintheta+costheta)=(pi)/(2)`
`rArr" "sintheta+costheta=(1)/(2)`
`rArr" "(1)/(sqrt(2))*sintheta+(1)/(sqrt(2))*costheta=(1)/(2sqrt(2))`
`rArr" "sintheta*sin""(pi)/(4)+costheta*cos""(pi)/(4)=(1)/(2sqrt(2))`
`therefore" "cos(theta-(pi)/(4))=(1)/(2sqrt(2))`
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