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If 3 sin2 A + 2 sin2 B = 1 and 3 sin 2A − 2 sin 2B = 0, where A and B are acute angles then find the value of (A +2B)

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5 years ago

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```										Dear Nirabhra,
sin2B=3/2sin2A 	                                         …(i)
And 	from the first equation,
3sin2A=1-2sin2B=cos2B 	           …(ii)
cos 	(A + 2B) = cos A. cos 2B – sin A.sin 2B
3cosA.sin2A-32sinA.sin2A
3cosA.sin2A-3sin2AcosA 	=0
cos (A+2B)=0
∴ 	                                      A+2B=π2,3π2                  	                 …(iii)
Given 	that < A < π/2 	and 0 < B < π/2
⇒ 	                                  0<A+2B<π+π2
⇒ 	                                  0<A+2B<3π2 …(iv)
∴ From 	(iii) and (iv),
A+2B=π2

All the best.
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```
5 years ago

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