Question 30 - CBSE Class 10 Sample Paper for 2024 Boards - Maths Standard - Solutions of Sample Papers for Class 10 Boards

Last updated at July 21, 2026 by Teachoo

If 1+sin^2⁡θ=3sin⁡θcos⁡θ, then prove that tan⁡θ=1 or 1/2

[Maths] If 1 + sin^2θ = 3sinθ cosθ , then prove that tanθ = 1 or 1/2 - CBSE Class 10 Sample Paper for 2024 Boards - Maths Standard

part 2 - Question 30 - CBSE Class 10 Sample Paper for 2024 Boards - Maths Standard - Solutions of Sample Papers for Class 10 Boards - Class 10

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Transcript

1+sin^2⁡𝜃=3 sin⁡〖𝜃 cos⁡𝜃 〗 Dividing by 〖𝒄𝒐𝒔〗^𝟐 𝜽 on both sides 1/(〖𝑐𝑜𝑠〗^2 𝜃) + sin^2⁡𝜃/(〖𝑐𝑜𝑠〗^2 𝜃) = (3 sin⁡〖𝜃 cos⁡𝜃 〗)/(〖𝑐𝑜𝑠〗^2 𝜃) 〖𝒔𝒆𝒄〗^𝟐 𝜽 + 〖𝑡𝑎𝑛〗^2 𝜃 = 3 tan 𝜃 Putting 〖𝒔𝒆𝒄〗^𝟐 𝜽 = 1 + 〖𝑡𝑎𝑛〗^2 𝜃 1 + 〖𝒕𝒂𝒏〗^𝟐 𝜽+ 〖𝑡𝑎𝑛〗^2 𝜃 = 3 tan 𝜃 1 + 2 〖𝑡𝑎𝑛〗^2 𝜃 = 3 tan 𝜃 Putting tan 𝜽 = x 1 + 2𝑥^2 = 3x 2𝒙^𝟐 – 3x + 1 = 0 Solving by Spitting the middle term 2𝑥^2 – 2x – x + 1 = 0 2𝑥(x – 2) -1(x – 2) = 0 (2x – 1)(x - 2) = 0 Therefore, x = 𝟏/𝟐 , x = 2 Replacing x = tan 𝜃 back we get, tan 𝜽 = 𝟏/𝟐 or 2 Hence proved

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