# Solve  sinx - cosx = 0?

Apr 18, 2017

$x = \frac{\pi}{4} + n \pi$

#### Explanation:

We have:

$\sin x - \cos x = 0$

Which we can rearrange as follows:

$\therefore \sin x = \cos x$

$\therefore \sin \frac{x}{\cos} x = 1$

$\therefore \tan x = 1$

$\therefore x = \left(\arctan 1\right) + n \pi \setminus \setminus$ where $n \in \mathbb{Z}$
$\therefore x = \frac{\pi}{4} + n \pi$
{"ft_lang_label":"__label__en","ft_lang_prob":0.5067952,"math_prob":1.0000099,"size":394,"snap":"2023-40-2023-50","text_gpt3_token_len":147,"char_repetition_ratio":0.14102565,"word_repetition_ratio":0.09090909,"special_character_ratio":0.4137056,"punctuation_ratio":0.1923077,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":1.0000099,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-12-06T20:38:41Z\",\"WARC-Record-ID\":\"<urn:uuid:f83a0b1c-1ced-4c73-8873-6f12a32fe29a>\",\"Content-Length\":\"33011\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:c70fc405-15af-4d8a-bcdc-bf6149ebcdd9>\",\"WARC-Concurrent-To\":\"<urn:uuid:3e10801f-8a6c-4bb0-8946-cc25860af337>\",\"WARC-IP-Address\":\"216.239.36.21\",\"WARC-Target-URI\":\"https://socratic.org/questions/58f66b0eb72cff6d065f28c0\",\"WARC-Payload-Digest\":\"sha1:ORDR2W62XMS47CDTGIIXGMHXPKA6J2D6\",\"WARC-Block-Digest\":\"sha1:4BZVIHUSX2HKCNTD67MKUKUTUOM7UC2O\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-50/CC-MAIN-2023-50_segments_1700679100603.33_warc_CC-MAIN-20231206194439-20231206224439-00185.warc.gz\"}"}