sin x + cos x =2 cos x
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It is particular value for case
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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
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