Math, asked by meliskameintjes1936, 9 months ago

The equation x=sin(y+5)sin(y+3)−sin2(y+4) represents

Answers

Answered by Swarup1998
2

Given: x=sin(y+5)sin(y+3)-sin^{2}(y+4)

Solution:

Now, x=sin(y+5)sin(y+3)-sin^{2}(y+4)

\Rightarrow 2x=2sin(y+5)sin(y+3)-2sin^{2}(y+4)

\Rightarrow 2x=cos(y+5-y-3)-cos(y+5+y+3)-2sin^{2}(y+4)

\Rightarrow 2x=cos2-cos(2y+8)-2sin^{2}(y+4)

\Rightarrow 2x=cos2-cos2(y+4)-2sin^{2}(y+4)

\Rightarrow 2x=cos2-1+2sin^{2}(y+4)-2sin^{2}(y+4)

\Rightarrow 2x=cos2-1

This is clearly a straight line of the form x = k i.e. parallel to the y -axis.

Answer: the given equation represents a straight line parallel to the y -axis.

To remember:

  • 2sinAsinB=cos(A-B)-cos(A+B)
  • cos2A=1-2sin^{2}A
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