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Algebra Difficulty 2.5 Junior Find the answer

Given sin⁡(θ−π4)=15\sin \left(\theta- \frac {\pi}{4}\right)= \frac {1}{5}, then cos⁡(θ+π4)=\cos \left(\theta+ \frac {\pi}{4}\right)=

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Solution

Solution: cos⁡(θ+π4)=sin⁡[π2−(θ+π4)]=sin⁡(π4−θ)=−sin⁡(θ−π4)=−15\cos \left(\theta+ \frac {\pi}{4}\right)=\sin \left[ \frac {\pi}{2}-(\theta+ \frac {\pi}{4})\right]=\sin \left( \frac {\pi}{4}-\theta\right)=-\sin \left(\theta- \frac {\pi}{4}\right)=- \frac {1}{5},
Therefore, the answer is: A\boxed{A}
This can be solved using the trigonometric identities.
This question tests the understanding of trigonometric identities and is considered a basic question.

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Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic and difficulty added by this site.