If cos⁡θ + cos⁡ 2 θ   = 1, the value of sin 2 ⁡θ + sin 4 ⁡θ is

(a) -1   (b) 0   (c) 1   (d) 2

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  1. Class 10
  2. Solutions of Sample Papers for Class 10 Boards

Transcript

Question 7 If cos⁡𝜃 + cos⁡𝜃 + cos⁡〖2 𝜃〗 = 1, the value of sin^2⁡𝜃 + sin^2⁡𝜃 is (a) −1 (b) 0 (c) 1 (d) 2 Given 𝑐𝑜𝑠⁡𝜃 + 〖𝑐𝑜𝑠〗^2⁡𝜃 = 1 𝑐𝑜𝑠⁡𝜃 = 1 − 〖𝒄𝒐𝒔〗^𝟐⁡𝜽 𝑐𝑜𝑠⁡𝜃 = 〖𝑠𝑖𝑛〗^2⁡𝜃 〖𝒔𝒊𝒏〗^𝟐⁡𝜽 = 𝒄𝒐𝒔⁡𝜽 Now, 〖𝑠𝑖𝑛〗^2⁡𝜃 + 〖𝑠𝑖𝑛〗^4⁡𝜃 = 𝒄𝒐𝒔⁡𝜽 + 〖𝒄𝒐𝒔〗^𝟐⁡𝜽 = 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.