## Trigonometry (11th Edition) Clone

$$\frac{\tan80^\circ-\tan(-55^\circ)}{1+\tan80^\circ\tan(-55^\circ)}=-1$$
$$X=\frac{\tan80^\circ-\tan(-55^\circ)}{1+\tan80^\circ\tan(-55^\circ)}$$ From the identity of the sum of tangent: $$\frac{\tan A-\tan B}{1+\tan A\tan B}=\tan(A-B)$$ So here $X$ actually follows the above identity with $A=80^\circ$ and $B=-55^\circ$. Therefore, $X$ can also be rewritten as $$X=\tan[80^\circ-(-55^\circ)]$$ $$X=\tan(80^\circ+55^\circ)$$ $$X=\tan135^\circ$$ We can rewrite $135^\circ$ as the difference of $180^\circ$ and $45^\circ$ $$X=\tan(180^\circ-45^\circ)$$ and apply the identity of tangent difference: $$X=\frac{\tan180^\circ-\tan45^\circ}{1+\tan180^\circ\tan45^\circ}$$ $$X=\frac{0-1}{1+0\times1}$$ $$X=\frac{-1}{1}=-1$$ Overall, $$\frac{\tan80^\circ-\tan(-55^\circ)}{1+\tan80^\circ\tan(-55^\circ)}=-1$$
{"ft_lang_label":"__label__en","ft_lang_prob":0.5311679,"math_prob":1.0000099,"size":826,"snap":"2022-05-2022-21","text_gpt3_token_len":313,"char_repetition_ratio":0.24817519,"word_repetition_ratio":0.0,"special_character_ratio":0.46731234,"punctuation_ratio":0.031446543,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":1.0000098,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-05-22T13:06:59Z\",\"WARC-Record-ID\":\"<urn:uuid:d8c6a5fc-57d7-4aaa-8910-0bd1fac88f46>\",\"Content-Length\":\"85403\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:4f060f82-824f-4271-8c81-bd23ab59b773>\",\"WARC-Concurrent-To\":\"<urn:uuid:8488ae40-cd16-4294-9f27-f10fcab24223>\",\"WARC-IP-Address\":\"44.198.198.134\",\"WARC-Target-URI\":\"https://www.gradesaver.com/textbooks/math/trigonometry/CLONE-68cac39a-c5ec-4c26-8565-a44738e90952/chapter-5-trigonometric-identities-section-5-4-sum-and-difference-identities-for-sine-and-tangent-5-4-exercises-page-227/28\",\"WARC-Payload-Digest\":\"sha1:DTTGYS4QTRI74RZTELQKRU3LZ46OHHCJ\",\"WARC-Block-Digest\":\"sha1:IN4QR65YKKQTQXPGKGTW7UL7IJ2IRM26\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-21/CC-MAIN-2022-21_segments_1652662545548.56_warc_CC-MAIN-20220522125835-20220522155835-00216.warc.gz\"}"}