541Let α, β be such π

Question

541Let α, β be such π < α - β < 3π. If sin α + sin β = -(21/65)and cos α + cos β-(27/65),then the value of cos(α-β/2) is  (A) -(3/√130) (B) (3/√130) (C) (6/65) (D) -(6/65)

Tardigrade Admin · Accepted Answer

Correct answer is (a) -(3/√130)

Q. $541 L e t α, β b es u c hπ < α - β < 3 π . I f s in α + s in β = - \frac{21}{65} an d cos α + cos β - \frac{27}{65}, t h e n t h e v a l u eo f cos \frac{α - β}{2} i s$

$- \frac{3}{130}$

$\frac{3}{130}$

$\frac{6}{65}$

$- \frac{6}{65}$

Correct answer is (a) $- \frac{3}{130}$

Q. 541Letα,βbesuchπ<α−β<3π.Ifsinα+sinβ=−6521​andcosα+cosβ−6527​,thenthevalueofcos2α−β​is

−130​3​

130​3​

656​

−656​