Question

sin x + cos x =2 cos x

Answer 1

It is particular value for case

Answer 2

Answer:

• Angle in 1st quadrant : x = π/4

• Principal solution : x = π/4 and 5π/4

• General solution : x = nπ + π/4 , n € Z

Note:

★ If sin∅ = sinα , then ;

∅ = nπ + (-1)ⁿα , n € Z

★ If cos∅ = cosα , then ;

∅ = 2nπ ± α , n € Z

★ If tan∅ = tanα , then ;

∅ = nπ + α , n € Z

Solution:

• Given : sinx + cosx = 2cosx
• To find : x = ?

We have ;

=> sinx + cosx = 2cosx

=> sinx = 2cosx - cosx

=> sinx = cosx

=> sinx / cosx = 1

=> tanx = 1

★ Angle in 1st quadrant :-

=> tanx = 1

=> tanx = tanπ/4

=> x = π/4

★ Principal solution :-

=> tanx = 1

=> tanx = tanπ/4 or tan(π + π/4)

=> tanx = tanπ/4 or tan5π/4

=> x = π/4 , 5π/4

★ General solution :-

=> tanx = 1

=> tanx = tanπ/4 ( Angle in 1st quadrant )

=> x = nπ + π/4 , n € Z