Find the general solution for given trigonometric equation sin2xcos2x+sin⁡xcos⁡x−1=0 The options are given in the...

Kelly Nelson

Kelly Nelson

Answered

2021-12-29

Find the general solution for given trigonometric equation
sin2xcos2x+sinxcosx1=0
The options are given in the form of tan1, so I tried to convert the equation completely in tan but was unable to do so.
I also tried using the identity of sin2x, through which I got
sin22x+2sin2x4=0
I have got no idea how to proceed further.

Answer & Explanation

Bukvald5z

Bukvald5z

Expert

2021-12-30Added 33 answers

Now,
(sin2x+1)2=5,
which is impossible because
0(sin2x+1)24
Joseph Fair

Joseph Fair

Expert

2021-12-31Added 34 answers

Hint
First set
u=sinxcosx
to obtain
u2+u1=0
then solve for x from u.
nick1337

nick1337

Expert

2022-01-08Added 573 answers

I'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.

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