Solving sin &#x2061;<!-- ⁡ --> &#x03B8;<!-- θ --> 2 </mfrac> + cos

Gaaljh

Gaaljh

Answered question

2022-06-10

Solving sin θ 2 + cos θ 2 = 2

Answer & Explanation

zalitiaf

zalitiaf

Beginner2022-06-11Added 27 answers

Notice:
cos ( θ 2 ) + sin ( θ 2 ) = 2 cos ( θ 2 ) 2 + 2 sin ( θ 2 ) 2 = 2 [ cos ( θ 2 ) 2 + sin ( θ 2 ) 2 ] =
2 [ sin ( π 4 ) cos ( θ 2 ) + cos ( π 4 ) sin ( θ 2 ) ] = 2 sin ( π 4 + θ 2 )
So:
cos ( θ 2 ) + sin ( θ 2 ) = 2
2 sin ( π 4 + θ 2 ) = 2
sin ( π 4 + θ 2 ) = 1
π 4 + θ 2 = π 2 + 2 π n
θ 2 = π 4 + 2 π n
θ = π 2 + 4 π n
Where n Z

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