Question

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

Answer 1

Step-by-step explanation:

Sin theta - cos theta=0

Sin theta=cos theta

Cos theta/sin theta=1

Cosec theta=1

Answer 2

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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