Math, asked by abhra12, 10 months ago

sin theta - cos theta = 0 then cosec theta = what​

Answers

Answered by ayush0919singh
0

Step-by-step explanation:

Sin theta - cos theta=0

Sin theta=cos theta

Cos theta/sin theta=1

Cosec theta=1

Answered by mysticd
0

Answer:

cosec\theta = cosec 45\degree = \sqrt{2}

Step-by-step explanation:

 Given \\sin\theta-cos\theta = 0\:--(1)

\implies (sin\theta-cos\theta)(sin\theta+cos\theta)= 0\times (sin\theta-cos\theta)

\implies sin^{2}\theta-cos^{2}\theta=0

\implies sin^{2}\theta - (1-sin^{2}\theta)=0

\implies sin^{2}\theta-1+sin^{2}\theta = 0

\implies 2sin^{2}\theta -1=0

\implies 2sin^{2}\theta = 1

\implies sin^{2}\theta = \frac{1}{2}

\implies sin^{2}\theta = \sqrt{\left(\frac{1}{2}\right)}

\implies sin\theta=\frac{1}{\sqrt{2}}\\=sin45 \degree

\implies \theta = 45\degree

\implies cosec 45 \degree =\frac{1}{sin 45 \degree}\\=\frac{1}{\frac{1}{\sqrt{2}}}\\=\sqrt{2}

Therefore,

cosec\theta = cosec 45\degree = \sqrt{2}

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