Sine rule, cosine rule and projection formula

JEE Main Mathematics · Properties of Triangle · 2 questions, latest first

• In a triangle ABC, BC=7, AC=8, AB=α ∈ N and cos A=2/3. If 49 cos (3 C)+42=m/n, where gcd(m, n)=1, then m+n is equal to ____.20246 April, Shift 2 · Q30
• In a triangle A B C, if cos A+2 cos B+ cos C=2 and the lengths of the sides opposite to the angles A and C are 3 and 7…202312 April, Shift 1 · Q19