‌+p‌cos‌Q ‌ [By projection formula ‌p=q‌cos‌R+r‌cos‌Q] ⇒‌q+p≥r ‌[‌ In triangle sum of two sides greater than third sides] ‌ ‌‌ So (b) is correct. ‌ (c) Bysine rule,
P=K‌sin‌p,q=K‌sin‌q,r=K‌sin‌R ‌
q+r
P
=‌
sin‌Q+sin‌R
sin‌P
≥‌
2√sin‌Q×sin‌R
sin‌P
‌‌[∵AM≥GM] So (c) is incorrect. (d) If p<q and q<r then p is smallest side, therefore one of Q or R be obtuse angle. So, one of cos‌Q or cos‌R can be negative. Therefore cos‌Q>‌