2. Use the Pythagorean identity: We know that: sin2x+cos2x=1 Substituting the expressions for sinx and cosx: (msiny)2+(ncosy)2=1 This simplifies to: m2sin2y+n2cos2y=1 3. Express cos2y in terms of sin2y: We can use the identity cos2y=1−sin2y: m2sin2y+n2(1−sin2y)=1 ...
Using the Pythagorean identity cos2y+sin2y=1, we have:9(cos2x+sin2x)+4(cos23x+sin23x)+12(cosxcos3x+sinxsin3x)=1 Step 3: Simplify using identitiesUsing the identity cos2θ+sin2θ=1:9(1)+4(1)+12(cos(x−3x))=1This simplifies to:9+4+12cos(−2x)=1Since cos(−2x)=cos...