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Properties of Triangle question

2021 · Shift 2 · Q21

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JEE Advanced
Mathematics
Properties of Triangle
2021 · Shift 2 · Q21

Properties of Triangle question

2021 · Shift 2 · Q21

JEE AdvancedMathematicsProperties of TriangleMultiple correct+4 / −2

Consider a triangle PQR having sides of lengths p, q and r opposite to the angles P, Q and R, respectively. Then which of the following statements is (are) TRUE?

A
$\cos P \ge 1 - {{{p^2}} \over {2qr}}$
B
$\cos R \ge \left( {{{q - r} \over {p + q}}} \right)\cos P + \left( {{{p - r} \over {p + q}}} \right)\cos Q$
C
${{q + r} \over p} \lt 2{{\sqrt {\sin q\sin R} } \over {\sin P}}$
D
If p < q and p < r, then $\cos Q \gt {p \over r}$ and $\cos R \gt {p \over q}$

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