CBSE Class 10 Sample Paper for 2022 Boards - Maths Standard [MCQ]

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Question 28 - CBSE Class 10 Sample Paper for 2022 Boards - Maths Standard [MCQ] - Solutions of Sample Papers for Class 10 Boards

Last updated at April 16, 2024 by

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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Transcript

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 has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.