Let `0lt=a , b , c ,dlt=pi,` where b and c are not complementary, such that `2cosa+6cosb+7cosc+9cosd=0` and `2sina-6sinb+7sinc-9sind=0,` then the value of `3(cos(a+d))/("cos"(b+c))` is_____

Single Choice Questions: 1.Let 0<=alpha, beta, gamma, delta,<=pi where beta and gamma are not complementary such that 2cos alpha+ 6 cos beta+7 cos gamma+9 cos delta=0 and 2 sin alpha- 6 sin beta+7 sin gamma-9 sin delta=0 if cos(alpha+delta)/cos(beta+gamma)=m/n when m and n are relatively prime positive numbers, then the value of (m+n) is equal to (A)11 (B)10 (C)9 (D)7

If cosA+cosB+cosC=0,sinA+sinB+sinC=0andA+B+C=180^(@) then the value of cos3A+cos3B+cos3C is :

If sinA+sin^2A=1, then the value of cos^2A+cos^4A is (a)2 (b) 1 (c) -2 (d) 0

Suppose A and B are two angles such that A , B in (0,pi) and satisfy sinA+sinB=1 and cosA+cosB=0. Then the value of 12cos2A+4cos2B is____

Suppose A and B are two angles such that A , B in (0,pi) and satisfy sinA+sinB=1 and cosA+cosB=0. Then the value of 12cos2A+4cos2B is____

If A and B are complementary angles, then (a) sinA=cosB (b) cosA=sinB (c) tanA=cotB (d) secA=cos e c\ B

If A, B, C, D be the angles of acyclic quadrilateral, show that : cosA +cosB+cosC+cosD=0 .

If A+B+C= pi/2 , show that : cos^2 A + cos^2 B + cos^2 C = 2 + 2 sinA sinB sinC .

If A,B,C,D are the angles of a cyclic quadrilateral, show that cosA+cosB+cosC+cosD=0

Let A , B , C be the three angles such that A+B+C=pi . If T a nAtanB=2, then find the value of (cos(A-B))/(cosC)