If-and-satisfy-sin-cos-1-2-then-the-greatest-value-of-2cos-sin-

Question Number 27821 by bmind4860 last updated on 15/Jan/18

I f α a n d β s a t i s f y s i n α c o s β = - \frac{1}{2} t h e n

t h e g r e a t e s t v a l u e o f 2 c o s α s i n β

Answered by ajfour last updated on 15/Jan/18

\sin α \cos β = - \frac{1}{2}

\Rightarrow 2 \sin α \cos β = - 1

\Rightarrow \sin (α + β) + \sin (α - β) = - 1

g r e a t e s t v a l u e o f \sin (α + β) = 0

w h e n \sin (α - β) = - 1

a n d 2 \sin (α + β) = 2 \sin α \cos β

+ 2 \cos α \sin β

s o 2 \cos α \sin β = 2 \sin (α + β) + 1

g r e a t e s t v a l u e o f

2 \cos α \sin β = 1 .

Commented by bmind4860 last updated on 15/Jan/18

g r e a t! t h i s i s t h e b e s t a n d f a r b e t t e r s o l u t i o n f r o m

t h a t l e n t h y s o l u t i o n o f d i f f e r e n t i a t i o n .

Commented by bmind4860 last updated on 15/Jan/18

r e a l l y s o m e t i m e s j u s t a n a l y z i n g t h e p r o b l e m

g i v e s e a s i e s t s o l u t i o n

t h a n k y o u! a g a i n

Commented by ajfour last updated on 15/Jan/18

w e l c o m e s i r! t h a n k y o u t o o,

a n d P r a k a s h S i r, w h o h a d

f o u n d e r r o r i n m y i n i t i a l

w r o n g a n s w e r .

Commented by bmind4860 last updated on 15/Jan/18

s i r c a n y o u p l e a s e h e l p m e i n t h e n e w

q u e s t i o n s p o s t e d b y m e