If a^2+b^2+c^2=1, then prove that |a^...

If `a^2+b^2+c^2=1,` then prove that `|a^2+(b^2+c^2)cosvarphia b(1-cosvarphi)a c(1-cosvarphi)b a(1-cosvarphi)b^2+(c^2+a^2)cosvarphib c(1-cosvarphi)c a(1-cosvarphi)c b(1-cosvarphi)c^2+(a^2+b^2)cosvarphi|` is independent of `a ,b ,cdot`

Similar Questions

Explore conceptually related problems

Evaluate: int(2sin2varphi-cosvarphi)/(6-cos^2varphi-4\ sinvarphi)\ dvarphi

Factors of cos4theta-cos4varphi are- a. (costheta+cosvarphi) b. \ (costheta-cosvarphi) c. ("costheta"+"sin") d. (costheta-s invarphi)

Prove that |(1,a,a^2),(1,b,b^2),(1,c,c^2)|=(a-b)(b-c)(c-a)

Prove that =|1 1 1a b c b c+a^2a c+b^2a b+c^2|=2(a-b)(b-c)(c-a)

If a^(2),b^(2),c^(2) are in AP then prove that (1)/(a+b),(1)/(c+b),(1)/(a+c) are also in AP.

If a + b + c = 0 , prove that a^(4) + b^(4) + c^(4) = 2(b^(2)c^(2)+c^(2)a^(2)+a^(2)b^(2)) = 1//2 (a^(2) + b^(2) + c^(2))^(2)

Prove that |{:(1,b,c),(a^(2),b^(2),c^(2)),(b+c,c+a,a+b):}|=(a-b)(b-c)(a+b+c)

If a, b, c, d are in GP, then prove that 1/((a^(2)+b^(2))), 1/((b^(2)+c^(2))), 1/((c^(2)+d^(2))) are in GP.

If a b+b c+c a=0 , then what is the value of (1/(a^2-b c)+1/(b^2-c a)+1/(c^2-a b)) ? (a) 0 (b) 1 (c) 3 (d) a+b+c