Prove that for A-B- - 2 - 2 -cos A-B 2 -cos A -cos B 2

R.T.P cos(A+B2) ≥cos A+cos B2 ⇒cos(A+B2) 12(cos A+cos B) ≥ 0 ⇒cos(A+B2) 12× 2cosA+B2cosA B2≥ 0 ⇒cos( A+B2) cos(A+B2)cos(A B2) ≥ 0 But co ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

General Solution of Trigonometric Equation

Prove that fo...

Question

Prove that for $A, B \in (- \frac{π}{2}, \frac{π}{2}), cos (\frac{A + B}{2}) \geq \frac{cos A + cos B}{2}$

Open in App

Solution

Suggest Corrections

Similar questions

If A+B+C = $π$ , prove that cos A + cos B - cos C = $(4 cos \frac{A}{2} cos \frac{B}{2} sin \frac{C}{2}) - 1$

Prove that $\frac{1 - cos A + cos B - cos (A + B)}{1 + cos A - cos B - cos (A + B)} = tan \frac{A}{2} cot (\frac{B}{2})$ .

If $A + B = \frac{π}{3}$ and $c o s A + c o s B = 1$
then find the value of $c o s \frac{A - B}{2}$

A + B = \frac{π}{3}

c o s A + c o s B = 1

cos \frac{(A - B)}{2}

A + B + C = π

cos (A / 2) + cos (B / 2) - cos (C / 2)

= 4 cos \frac{π + A}{4} cos \frac{π + B}{4} cos \frac{π - C}{4}

Join BYJU'S Learning Program