+0

# Trignometery

0
139
1

If A is an acute angle such that tan A + sec A = 3, then find cos A.

Jun 25, 2022

#1
+1

tan A + sec A =   3            {  tan^2 A + 1  =  sec^2 A  →    tan^2 A = sec^2 A - 1  → tan A = sqrt [ sec^2 A - 1]  }

sqrt [ sec^2A -1 ] + sec A  = 3

sqrt [sec^2A  - 1 ]  = 3  - sec A             square both sides

sec^2 A   - 1  =  9 - 6sec A + sec^2 A     rearrange as

6sec  A  =  10

sec  A  = 10   / 6     =    5/ 3

cos A  =  1 /sec A  =  1  /(5/3) =   3 / 5 Jun 25, 2022
{"ft_lang_label":"__label__en","ft_lang_prob":0.65346533,"math_prob":0.9999651,"size":364,"snap":"2023-14-2023-23","text_gpt3_token_len":175,"char_repetition_ratio":0.23333333,"word_repetition_ratio":0.05357143,"special_character_ratio":0.5631868,"punctuation_ratio":0.021505376,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99973613,"pos_list":[0,1,2,3,4,5,6],"im_url_duplicate_count":[null,null,null,null,null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-06-06T02:49:24Z\",\"WARC-Record-ID\":\"<urn:uuid:b04f31f3-2164-49b2-9b41-254216c86274>\",\"Content-Length\":\"21621\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:37325d24-f8b4-41a1-81af-eec7085f17e3>\",\"WARC-Concurrent-To\":\"<urn:uuid:2f58280a-08da-4bf4-9c0b-d94977c19639>\",\"WARC-IP-Address\":\"49.12.76.224\",\"WARC-Target-URI\":\"https://web2.0calc.com/questions/trignometery_1\",\"WARC-Payload-Digest\":\"sha1:VREBBMDWQRLMBMTWJIUIWJNT7ZV5PBSV\",\"WARC-Block-Digest\":\"sha1:RKEHAINDFT4UQKEWGEQDSV4FMRFDB6HY\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-23/CC-MAIN-2023-23_segments_1685224652207.81_warc_CC-MAIN-20230606013819-20230606043819-00024.warc.gz\"}"}