Test Index

CBSE Class 12 Math 2023 All Sets Solved Paper

© examsnet.com
Question : 19 of 20
Marks: +1, -0
Assertion(A): If a line makes angles α, β, γ with positive direction of the coordinate axes, then sin⁡2α+sin⁡2β+sin⁡2γ=2.\sin^2\alpha+\sin^2\beta + \sin^2\gamma = 2.
Reason(R) : The sum of squares of the direction cosines of a line is 1.
Solution:  
If a line makes angles α, β, γ with positive direction of the coordinate axes, then cos⁡2α+cos⁡2β+cos⁡2γ=1\cos^2\alpha + \cos^2\beta + \cos^2\gamma = 1
⇒(1−sin⁡2α)+(1−sin⁡2β)+(1−sin⁡2γ)=1\Rightarrow (1-\sin^2\alpha) + (1 - \sin^2\beta) + (1 - \sin^2\gamma) = 1
⇒sin⁡2α+sin⁡2β+sin⁡2γ=2\Rightarrow \sin^2\alpha + \sin^2\beta + \sin^2\gamma = 2
Both (A) and (R) are true and (R) is the correct explanation of (A).
© examsnet.com
Go to Question:
Prev Question
Next Question