Find the general solution for given trigonometric equation sin2xcos2x+sin⁡xcos⁡x−1=0 The options are given in the form of tan−1, so I tried to convert the equation completely in tan but was unable to do so. I also tried using the identity of sin⁡2x, through which I got sin22x+2sin⁡2x−4=0 I have got no idea how to proceed further.

Question

Find the general solution for given trigonometric equation  sin2xcos2x+sin⁡xcos⁡x−1=0  The options are given in the form of tan−1, so I tried to convert the equation completely in tan but was unable to do so.  I also tried using the identity of sin⁡2x, through which I got   sin22x+2sin⁡2x−4=0   I have got no idea how to proceed further.

Bukvald5z · Accepted Answer

Now,  (sin⁡2x+1)2=5,  which is impossible because  0≤(sin⁡2x+1)2≤4

Joseph Fair · Accepted Answer

Hint  First set  u=△sin⁡xcos⁡x  to obtain  u2+u−1=0  then solve for x from u.

nick1337 · Accepted Answer

I&#039;m sorry, but this quadratic equation has −1±5 as roots, and the absolute value of each of these roots is greater than 1. Therefore as a trigonometric equation in x, it has no root.