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

Slide57.jpeg

Sample paper Maths Class 10 - 2022 Boards - Standard.jpg

Learn in your speed, with individual attention - Teachoo Maths 1-on-1 Class


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)

Ask a doubt
Davneet Singh's photo - Co-founder, Teachoo

Made by

Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.