Question

sin theta+cosec theta= 2 find sin^2 + cosec^2 withoudt using identities

Answer 1

Answer:

your answer attached in the photo

Answer 2

$\color{orange}\huge{\mathfrak{given}}$

$sin \: theta + cosec \: theta = 2$

$\color{cyan}\huge{\mathfrak{to \: find}}$

${sin}^{2} + {cosec} ^{2}$

$\color{magenta}\huge{\mathfrak{answer}}$

As we know that,

$cosec\: theta \: = \frac{1}{sin \: theta}$

Therefore,

$sin \: theta + \frac{1}{sin \: theta} = 2$

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

${sin}^{2}theta - {1 } ^{2} = 0$

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

$sin \: theta \: = 1$

Now,

${sin }^{2} theta + {cosec}^{2} theta$

$= {sin }^{2} theta + \frac{1}{sin ^{2} \: theta}$

$= 1 + 1$

$= 2$

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