Question

sinx+cosx=sin2x-1
Find its general solution.

Answer 1

Answer:

Hey mate here is ur answer

Step-by-step explanation:

Arc x = 0;

x

=

π

4

;

x

=

π

2

;

x

=

π

Explanation:

1 - sin 2x = cos x - sin x

Square both sides:

(

1

−

sin

2

x

)

2

=

(

cos

x

−

sin

x

)

2

1

−

2

sin

2

x

+

sin

2

2

x

=

cos

2

x

+

sin

2

x

−

2

sin

x

.

cos

x

1

−

2

sin

2

x

+

sin

2

2

x

=

1

−

sin

2

x

sin

2

2

x

−

sin

2

x

=

0

sin 2x (sin 2x - 1) = 0

a. sin 2x = 0

sin 2x= 0 --> 2x = 0 --> x = 0

sin 2x = 0 -->

2

x

=

π

-->

x

=

π

2

sin 2x = 0 -->

2

x

=

2

π

-->

x

=

π

b. sin 2x = 1 -->

2

x

=

π

2

-->

x

=

π

4

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