Letα,β be such that π

Question

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

Tardigrade Admin · Accepted Answer

Correct answer is (c) -(3/√130)

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

$\frac{6}{65}$

$\frac{3}{130}$

$- \frac{3}{130}$

$- \frac{6}{65}$

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

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

656​

130​3​

−130​3​

−65​6​

Correct answer is (c) −130​3​

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

$\frac{6}{65}$

$\frac{3}{130}$

$- \frac{3}{130}$

$- \frac{6}{65}$

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