How to Solve 1 + sin 2x = ( sin 3x – cos 3x )whole square
How to Solve 1 + sin 2x = ( sin 3x – cos 3x )whole square
Mohammed Saleem Mohiuddin , 9 Years ago
Grade 12th pass
Trigonometry> How to Solve 1 + sin 2x = ( sin 3x – cos ...
3 AnswersBijoy Deka
1 + sin 2x = ( sin 3x – cos 3x )2
1 + sin 2x = sin2 3x + cos2 3x – 2sin3x. cos3x
1 + sin 2x = 1 – 2sin3x. cos3x (Since sin2 A + cos2 A = 1)
sin 2x = – sin 6x ( sin 2A = 2sinAcosA)
sin 6x = – sin 2x
sin 6x = sin (π + 2x) ( Since sin (π + A) = – sin A)
6x = nπ – (π + 2x) or 6x = 2nπ + (π + 2x) n ∈ Z
6x + 2x = (n-1)π or 6x -2x = (2n+1)π n ∈ Z
8x = (n-1)π or 4x = (2n +1)π n ∈ Z
x = (n-1)π / 8 or x = (2n +1)π /4 n ∈ Z
Ajay
Wrong question
Suppose x = 30 Degrees
Then LHS = 1 + sin60 = 1 + sqrt(3) /2
RHS = (sin 90 – cos 90)2 = 1
Hence question is wrong
Bijoy Deka
This is not an Identity. It is an equation. Equations are called identities, if they are satisfied by all values of the unknown angles for which the functions are defined.
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