Question

find a and b if sin(a+2b)=root3/2 and cos(a+b)=1/2

Answer 1

HELLO DEAR,

GIVEN THAT:-

sin(a + 2b) = √3/2

⇒sin(a + 2b) = sin60
∴ [ sin60 = √3/2 ]

⇒a + 2b = 60----------( 1 )

cos(a + b) = 1/2

⇒cos(a + b) =cos60
∴ [ cos60 = -1/2 ]

⇒a + b = 60----------( 2 )

from-----( 1 ) & -----( 2 )

a + 2b = 60
a + b = 60
(-)__(-)__(-)
------------------
b = 0 [ put in ---( 1 ) ]

a + 2(0) = 60

⇒a = 60 , b = 0

I HOPE ITS HELP YOU DEAR,
THANKS

Answer 2

Hii friend,

Sin (a+2b) = ✓3/2

Sin(a+2b) = Sin 60°

a+2b = 60........(1)

Cos (a+b) = 1/2

Cos (a+b) = Cos60

a+b = 60.......(2)

Subtract equation (1) from equation (2)

a+2b = 60
a+b = 60
__________

b = 0



Putting the value of B in (2)

a+b = 60

a+0 = 60

a= 60-0

a = 60°.

HOPE IT WILL HELP YOU...... :-)