If cot θ = sin 2θ, where θ ≠ nπ, n is integer then θ equals to

1. 45 and 60
2. 45 and 90
3. 45 only
4. 90 only

Option 2 : 45 and 90

Detailed Solution

Formula used:

sin 2θ = 2sin θ.cos θ

$$\frac{cos\ θ}{sin\ θ}\ = \ cot\ \theta$$

Calculation:

Given that,

cot θ = sin 2θ,

where θ ≠ nπ, n is an integer

⇒ $$\frac{cos\ θ}{sin\ θ}\ =\ 2sin\ θ.cos\ θ$$

⇒ cos θ.(2sin2θ - 1) = 0

Case:1 cos θ = 0

⇒ θ = 90

Case:2 (2sin2θ - 1) = 0

⇒ sin θ = 1/√2

⇒ θ = 45∘
{"ft_lang_label":"__label__en","ft_lang_prob":0.76370955,"math_prob":1.0000019,"size":2584,"snap":"2022-05-2022-21","text_gpt3_token_len":948,"char_repetition_ratio":0.11550388,"word_repetition_ratio":0.04528302,"special_character_ratio":0.34868422,"punctuation_ratio":0.094076656,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":1.0000017,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-01-21T23:08:19Z\",\"WARC-Record-ID\":\"<urn:uuid:476a26de-9fa6-4a10-bb79-54a21e34855a>\",\"Content-Length\":\"115994\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:12df9721-b817-4e19-b190-e2cdcfd257cb>\",\"WARC-Concurrent-To\":\"<urn:uuid:610b2c2d-b1fc-4c17-8aa9-76f12e78e79a>\",\"WARC-IP-Address\":\"172.67.30.170\",\"WARC-Target-URI\":\"https://testbook.com/question-answer/if-cot-sin-2-whereth--619e40e683cf4ef0fc246c0d\",\"WARC-Payload-Digest\":\"sha1:ITLX7T5E4E3DEZCRGX5LTSCCC3QN2MJM\",\"WARC-Block-Digest\":\"sha1:45JKGC4VFFBFHVPXTDLN6PNOKIQNYJIZ\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-05/CC-MAIN-2022-05_segments_1642320303717.35_warc_CC-MAIN-20220121222643-20220122012643-00062.warc.gz\"}"}