TS EAMCET · Maths · Straight Lines

By rotating the coordinate axes in the positive direction about the origin by an angle $α$ , if the point $(1, 2)$ is transformed to $(\frac{3 \sqrt{3} - 1}{2 \sqrt{2}}, \frac{\sqrt{3} + 3}{2 \sqrt{2}})$ in new coordinate system, then $α =$

A $\frac{π}{3}$
B $\frac{π}{6}$
C $\frac{π}{9}$
D $\frac{π}{12}$

Verified Solution

Answer & Solution

Correct Answer

(D) $\frac{π}{12}$

Step-by-step Solution

Detailed explanation

Given that x,y=1,2 x',y'=33-122,3+322 ⇒x'=xcosα+ysinα;y'=-xsinα+ycosα 33-122=1cosα+2sinα ...1 3+322=-1sinα+2cosα ...2 Now, adding equations (1)+(2), 33-122+23+322=cosα+2sinα-2sinα+4cosα…

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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By rotating the coordinate axes in the positive direction about the origin by an angle α, if the point 1,2 is transformed to 33-122,3+322 in new coordinate system, then α=

Step-by-step Solution

By rotating the coordinate axes in the positive direction about the origin by an angle $α$ , if the point $(1, 2)$ is transformed to $(\frac{3 \sqrt{3} - 1}{2 \sqrt{2}}, \frac{\sqrt{3} + 3}{2 \sqrt{2}})$ in new coordinate system, then $α =$