What is the value of [(sin4x + sin4y) × tan(2x – 2y)] / (sin4x – sin4y)?
What is the value of [(sin4x + sin4y) × tan(2x – 2y)] / (sin4x – sin4y)?
1). tan2(2x + 3y)
2). tan2
3). cot(x – y)
4). tan(2x + 2y)
1 answers
[(sin4x + sin4y) × tan(2x – 2y)] / (sin4x – sin4y)
$(\Rightarrow \frac{{2\sin \left( {\frac{{4x\; + \;4y}}{2}} \right)\sin \left( {\frac{{4x\; - \;4y}}{2}} \right)\tan \left( {2x\; - \;2y} \right)}}{{2cos\left( {\frac{{4x\; + \;4y}}{2}} \right)cos\left( {\frac{{4x\; - \;4y}}{2}} \right)}})$
$(\Rightarrow \frac{{{\rm{sin}}\left( {2x\; + \;2y} \right){\rm{cos}}\left( {2x\; - \;2y} \right){\rm{tan}}\left( {2x\; - \;2y} \right)}}{{{\rm{cos}}\left( {2x\; + \;2y} \right){\rm{sin}}\left( {2x\; - \;2y} \right)}})$
$(\Rightarrow tan2\left( {x\; + \;y} \right)\frac{1}{{{\rm{tan}}\left( {2x - 2y} \right)}}{\rm{tan}}\left( {2x - 2y} \right))$
⇒ tan2(x + y) = tan(2x + 2y)
∴ [(sin4x + sin4y) × tan(2x – 2y)] / (sin4x – sin4y) = tan(2x + 2y)Other Questions
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