If 1+ sin2α = 3 sinα cosα, then values of cotα are
(a) −1, 1 (b) 0, 1 (c)1, 2 (d) −1, −1
CBSE Class 10 Sample Paper for 2022 Boards - Maths Standard [MCQ]
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CBSE Class 10 Sample Paper for 2022 Boards - Maths Standard [MCQ]
Last updated at Sept. 6, 2021 by Teachoo
Question 28 If 1+ sin2𝛼 = 3 sin𝛼 cos𝛼, then values of cot𝛼 are (a) −1, 1 (b) 0, 1 (c)1, 2 (d) −1, −1 Now, 1 + sin^2𝛼 = 3 sin𝛼 cos𝛼 Putting 〖𝒔𝒊𝒏〗^𝟐𝜶 + 〖𝒄𝒐𝒔〗^𝟐𝜶 = 1 〖𝒔𝒊𝒏〗^𝟐𝜶 + 〖𝒄𝒐𝒔〗^𝟐𝜶 + sin^2𝛼 = 3 sin𝛼 cos𝛼 2 〖𝑠𝑖𝑛〗^2𝛼 + 〖𝑐𝑜𝑠〗^2𝛼 = 3 𝑠𝑖𝑛𝛼 𝑐𝑜𝑠𝛼 2 〖𝑠𝑖𝑛〗^2𝛼 + 〖𝑐𝑜𝑠〗^2𝛼 − 3 𝑠𝑖𝑛𝛼 𝑐𝑜𝑠𝛼 = 0 𝟐 〖𝒔𝒊𝒏〗^𝟐𝜶 − 3 𝒔𝒊𝒏𝜶 𝒄𝒐𝒔𝜶 + 〖𝒄𝒐𝒔〗^𝟐𝜶 = 0 2 〖𝑠𝑖𝑛〗^2𝛼 − 2 𝑠𝑖𝑛𝛼 𝑐𝑜𝑠𝛼 − 𝑠𝑖𝑛𝛼 𝑐𝑜𝑠𝛼 + 〖𝑐𝑜𝑠〗^2𝛼 = 0 2 𝑠𝑖𝑛𝛼 "(" 𝑠𝑖𝑛𝛼 − 𝑐𝑜𝑠𝛼) − 𝑐𝑜𝑠𝛼 "(" 𝑠𝑖𝑛𝛼 − 𝑐𝑜𝑠𝛼) = 0 "(" 𝟐 𝒔𝒊𝒏𝜶 − 𝒄𝒐𝒔𝜶) "(" 𝒔𝒊𝒏𝜶 − 𝒄𝒐𝒔𝜶) = 0 𝟐 𝒔𝒊𝒏𝜶 − 𝒄𝒐𝒔𝜶 = 0 2 𝑠𝑖𝑛𝛼 = 𝑐𝑜𝑠𝛼 𝑐𝑜𝑠𝛼 "= " 2 𝑠𝑖𝑛𝛼 𝑐𝑜𝑠𝛼/sin𝛼 "= " 2 𝐜𝐨𝐭 𝜶 "= " 𝟐 𝒔𝒊𝒏𝜶 − 𝒄𝒐𝒔𝜶 = 0 𝑠𝑖𝑛𝛼 = 𝑐𝑜𝑠𝛼 𝑐𝑜𝑠𝛼 "= " 2 𝑠𝑖𝑛𝛼 𝑐𝑜𝑠𝛼/sin𝛼 "= " 1 𝐜𝐨𝐭 𝜶 "= " 𝟏 So, the correct answer is (c)