AP EAMCET · Maths · Properties of Triangles

In any \(\triangle A B C, \frac{\cos 2 A}{a^2}-\frac{\cos 2 B}{b^2}=\)

A \(a^2-b^2\)
B \(\frac{1}{a^2}-\frac{1}{b^2}\)
C \(a^2+b^2\)
D \(\frac{1}{a^2}+\frac{1}{b^2}\)

Verified Solution

Answer & Solution

Correct Answer

(B) \(\frac{1}{a^2}-\frac{1}{b^2}\)

Step-by-step Solution

Detailed explanation

\begin{aligned} & \frac{\cos 2 A}{a^2}-\frac{\cos 2 B}{b^2}=\frac{1-2 \sin ^2 A}{a^2}-\frac{1-2 \sin ^2 B}{b^2} \\ & =\frac{1}{a^2}-\frac{1}{b^2}-2\left[\frac{\sin ^2 A}{a^2}-\frac{\sin ^2 B}{b^2}\right] \\ & =\frac{1}{a^2}-\frac{1}{b^2} \quad\left[\because \frac{\sin…

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.

Same subject

Let \(a_n=\frac{10^n}{n !}\) for \(n=1,2,3, \ldots\) then the greatest value of \(n\) for which \(a_n\) is the greatest is

AP EAMCET 2010 Medium

Match the following columns.

Column I	Column 11
(A) The centroid of the triangle formed by (2, 3,-1), (5, 6, 3),(2,-3,1) is	(p) (2,2,2)
(B) The circumcentre of the triangle formed by (1, 2, 3), (2, 3, 1),(3, 1, 2) is	(q) (3, 1, 4)
(C) The orthocentre of the triangle formed by (2, 1, 5), (3, 2, 3), (4, 0, 4) is	(r) (1, 1, 0)
(D) The incentre of the triangle formed by (0, 0, 0), (3, 0, 0), (4, 0, 4) is	(s) (3, 2, 1)
(E) The incentre of the triangle formed by (0, 0, 0), (3, 0, 0), (4, 0, 4) is	(t) (0, 0, 0)

AP EAMCET 2015 Hard

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