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  • <img alt="if\ \sin \theta - \cos\theta=\frac{1}{\sqrt{2}}\ then\ find\ the\ value\ of\ \theta" src="https://learn.careers360.com/latex-image/?if%5C%20%5Csin%20%5Ctheta%20-%20%5Ccos%5Ctheta%3D%5Cfra

if\ \sin \theta - \cos\theta=\frac{1}{\sqrt{2}}\ then\ find\ the\ value\ of\ \theta

Option: 1

\frac{\pi}{4}


Option: 2

\frac{7\pi}{12}


Option: 3

\frac{5\pi}{12}


Option: 4

\frac{\pi}{12}


Answers (1)

best_answer

 

Allied Angles (Part 1) -

Allied Angles (Part 1)

 

Two angles or numbers are called allied iff their sum or difference is a multiple of π/2   

  • sin (900 - θ) = cos (θ)

  • cos (900 - θ) = sin (θ)

  • tan (900 - θ) = cot (θ)

  • csc (900 - θ) = sec (θ)          

  • sec (900 - θ) = csc (θ)

  • cot (900 - θ) = tan (θ)

 

  • sin (900 + θ) = cos (θ)

  • cos (900 + θ) = - sin (θ)

  • tan (900 + θ) = - cot (θ)

  • csc (900 + θ) = sec (θ)          

  • sec (900 + θ) = - csc (θ)

  • cot (900 + θ) = - tan (θ)

-

 

 

 

\sin \theta - \cos\theta=\frac{1}{\sqrt{2}}\\ \sqrt{2}(\frac{1}{\sqrt{2}}\sin\theta-\frac{1}{\sqrt{2}}\cos\theta)=\frac{1}{\sqrt{2}}\\ \sqrt{2}\ \sin(\theta-\frac{\pi}{4})=\frac{1}{\sqrt{2}}\\ \theta-\frac{\pi}{4}=\frac{\pi}{6}\\ \theta=\frac{5\pi}{12}

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