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avatar+108 

Q 5f no 6

 

If Sin Ø + Sin 2Ø = a, & Cos Ø + Cos 2Ø = b

Prove that (a2 + b2) (a2 + b2-3) =2 b

 

Sin Ø + Sin 2Ø = a

Let c = Ø+2Ø = 3Ø

and d = Ø-2Ø = -Ø

c + d = 2Ø

c - d = 4Ø

 

Therefore

a = 2 Sin Ø. Cos 2Ø

&

a2 = 4 Sin2 Ø. Cos22 Ø      

Cos Ø + Cos 2Ø = b

Let c = Ø+2Ø = 3Ø

and d = Ø-2Ø = -Ø

c + d = 2Ø

c - d = 4Ø

 

Therefore

b = 2 Cos Ø. Cos 2Ø

&

b2 = 4 Cos2 Ø. Cos22 Ø

 

 

a2 + b2 = 4 Sin2 Ø. Cos22 Ø + 4 Cos2 Ø. Cos22 Ø

=   4 Cos22 Ø (Sin2 Ø + Cos2 Ø) = 4 Cos22 Ø

Therefore (a2 + b2) (a2 + b2-3) =

4 Cos22Ø (4 Cos22 Ø-3) = 16 Cos4 2Ø – 12 Cos2

=4 Cos2Ø (4Cos32Ø – 3Cos 2Ø)

=4 Cos 2Ø. Cos 6Ø

 

2b = 4 Cos Ø. Cos 2Ø

Conclusion:

4 Cos Ø. Cos 2Ø = 4 Cos 2Ø. Cos 6Ø

 

CosØ =  Cos 6Ø  (??????)

 

 

 Feb 24, 2019

Best Answer 

 #1
avatar+27531 
+2

Prove as follows:

 

(Note: your expressions for a and b are incorrect).

 Feb 24, 2019
 #1
avatar+27531 
+2
Best Answer

Prove as follows:

 

(Note: your expressions for a and b are incorrect).

Alan Feb 24, 2019
 #2
avatar+108 
+1

Thanks for that Alan.  I had been following this factor theory ... Need to trace the fundamental mistake!

 

 

Regards and I re-assert that you do a great job !

 Feb 24, 2019

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