If 1+ sin⁡2α  = 3 sin⁡α  cos⁡α, then values of cot⁡α are

(a) −1, 1   (b) 0, 1   (c)1, 2   (d) −1, −1

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  1. Class 10
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Question 28 If 1+ sin⁡2𝛼 = 3 sin⁡𝛼 cos⁡𝛼, then values of cot⁡𝛼 are (a) −1, 1 (b) 0, 1 (c)1, 2 (d) −1, −1 Now, 1 + sin^2⁡𝛼 = 3 sin⁡𝛼 cos⁡𝛼 Putting 〖𝒔𝒊𝒏〗^𝟐⁡𝜶 + 〖𝒄𝒐𝒔〗^𝟐⁡𝜶 = 1 〖𝒔𝒊𝒏〗^𝟐⁡𝜶 + 〖𝒄𝒐𝒔〗^𝟐⁡𝜶 + sin^2⁡𝛼 = 3 sin⁡𝛼 cos⁡𝛼 2 〖𝑠𝑖𝑛〗^2⁡𝛼 + 〖𝑐𝑜𝑠〗^2⁡𝛼 = 3 𝑠𝑖𝑛⁡𝛼 𝑐𝑜𝑠⁡𝛼 2 〖𝑠𝑖𝑛〗^2⁡𝛼 + 〖𝑐𝑜𝑠〗^2⁡𝛼 − 3 𝑠𝑖𝑛⁡𝛼 𝑐𝑜𝑠⁡𝛼 = 0 𝟐 〖𝒔𝒊𝒏〗^𝟐⁡𝜶 − 3 𝒔𝒊𝒏⁡𝜶 𝒄𝒐𝒔⁡𝜶 + 〖𝒄𝒐𝒔〗^𝟐⁡𝜶 = 0 2 〖𝑠𝑖𝑛〗^2⁡𝛼 − 2 𝑠𝑖𝑛⁡𝛼 𝑐𝑜𝑠⁡𝛼 − 𝑠𝑖𝑛⁡𝛼 𝑐𝑜𝑠⁡𝛼 + 〖𝑐𝑜𝑠〗^2⁡𝛼 = 0 2 𝑠𝑖𝑛⁡𝛼 "(" 𝑠𝑖𝑛⁡𝛼 − 𝑐𝑜𝑠⁡𝛼) − 𝑐𝑜𝑠⁡𝛼 "(" 𝑠𝑖𝑛⁡𝛼 − 𝑐𝑜𝑠⁡𝛼) = 0 "(" 𝟐 𝒔𝒊𝒏⁡𝜶 − 𝒄𝒐𝒔⁡𝜶) "(" 𝒔𝒊𝒏⁡𝜶 − 𝒄𝒐𝒔⁡𝜶) = 0 𝟐 𝒔𝒊𝒏⁡𝜶 − 𝒄𝒐𝒔⁡𝜶 = 0 2 𝑠𝑖𝑛⁡𝛼 = 𝑐𝑜𝑠⁡𝛼 𝑐𝑜𝑠⁡𝛼 "= " 2 𝑠𝑖𝑛⁡𝛼 𝑐𝑜𝑠⁡𝛼/sin⁡𝛼 "= " 2 𝐜𝐨𝐭 𝜶 "= " 𝟐 𝒔𝒊𝒏⁡𝜶 − 𝒄𝒐𝒔⁡𝜶 = 0 𝑠𝑖𝑛⁡𝛼 = 𝑐𝑜𝑠⁡𝛼 𝑐𝑜𝑠⁡𝛼 "= " 2 𝑠𝑖𝑛⁡𝛼 𝑐𝑜𝑠⁡𝛼/sin⁡𝛼 "= " 1 𝐜𝐨𝐭 𝜶 "= " 𝟏 So, the correct answer is (c)

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.