Question

Cos3x-sin3x=(cosx+sinx)(1+2sin2x)

Answer 1

Answer:

cos3x - sin3x = ( cosx + sinx ) × ( 1 + 2sin2x)

4cosx³ - 3cosx - ( - 4sinx³ + 3sinx ) = ( cosx + sinx ) × ( 1 + 2 × 2sinxcosx)

4cosx³ - 3cosx + 4sinx³ - 3sinx  = ( cosx + sinx ) × ( 1 + 4sinxcosx)

4cosx³ - 3cosx + 4sinx³ - 3sinx  = cosx + 4cosx² sinx + sinx + 4sinx²cosx

4cosx³ - 3cosx + 4sinx³ - 3sinx - cosx - 4cosx² sinx - sinx - 4sinx²cosx = 0

4cosx³ - 4cosx + 4sinx³ - 4sinx - 4cosx² sinx - 4sinx²cosx = 0

- 4cosx × ( - cosx² + 1 ) + 4sinx³ - 4sinx - 4cosx² sinx - 4sinx²cosx = 0

- 4cosxsinx² + 4sinx³ - 4sinx - 4cosx² sinx - 4sinx²cosx = 0

4sinx × ( 2sinxcosx + sinx² - 1 - cosx² ) = 0

4sinx × ( - sin2x + sinx² - 1 - cosx² ) = 0

4sinx × ( - sin2x - ( 1 - sinx² ) - cosx² ) = 0

4sinx × ( - sin2x - cosx² - cosx² ) = 0

4sinx × ( - sin2x - 2cosx² ) = 0

- 4sinxsin2x - 8sinxcosx²  = 0

- 4sinx × sin2x + 2cosx²  = 0

sinx × sin2x + 2cosx²  = 0

sinx = 0

sin2x + 2cosx²  = 0

x = k π

x = π / 2 + k π

x = 3π / 4 + k π

x = kπ / 2

x = 3π / 4

Here is Your Solution.

Mark Brainliest

@manishthakur100

Answer 2

Answer:

see the attachment buddy