For all values of A, B and C, prove that:- cosA + cosB + cosC + cos (A+B+C)= 4cos (A + B/2). cos (B+C/2). cos (C+ A/2)

Open in App

Solution

Suggest Corrections

Similar questions

Q. Prove that

$\frac{c o s A}{c c o s B + b c o s C} + \frac{c o s B}{a c o s C + c c o s A} + \frac{c o s C}{a c o s B + b c o s A} = \frac{a^{2} + b^{2} + c^{2}}{2 a b c}$

Q. Prove that,

\frac{c - b c o s A}{b - c c o s A} = \frac{c o s B}{c o s C}

Q. Prove that

\frac{cos C + cos A}{c + a} + \frac{cos B}{b} = \frac{1}{b}

Q. Prove that

△ =

∣ ∣ ∣ ∣ \begin{matrix} s i n A & s i n B & s i n C c o s A & c o s B & c o s C c o s^{3} A & c o s^{3} B & c o s^{3} C \end{matrix} ∣ ∣ ∣ ∣

= sin(A-B) sin(B-C) sin(C-A) cos(A+B+C)
Also determine when

△ = 0.

Q. Let A, B, C are 3 angles such that

c o s A + c o s B + c o s C = 0

and if

c o s A c o s B c o s C = λ (c o s 3 A + c o s 3 B + c o s 3 C)

then

λ

is equal to

Join BYJU'S Learning Program