Question

of sin theta + cosec thetha=2 , then the value of sin^2018 +cosec^2018, is​

Answer 1

Given

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

To find

$\tt : \implies \: sin ^{2018} \theta + cosec ^{2018} \theta$

Now Simplify the equation

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

We Know that

$\tt : \implies cosec \theta = \dfrac{1}{sin \theta}$

we get

$\tt : \implies sin \theta + \dfrac{1}{sin \theta} - 2 = 0$

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

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

using this identities

$\tt : \implies(a - b )^{2} = {a}^{2} + {b}^{2} - 2ab$

we get

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

$\tt : \implies \: sin \theta - 1 = 0$

$\tt : \implies \: sin \theta = 1$

Now we have to Find

$\tt : \implies \: sin ^{2018} \theta + cosec ^{2018} \theta$

$\tt : \implies \: sin ^{2018} \theta + \dfrac{1}{sin^{2018} \theta}$

Now Put

$\tt : \implies \: sin \theta = 1$

we get

$\tt \: : \implies(1)^{2018} + (1)^{2018}$

$\tt : \implies \: 1 + 1 =2$

Answer is 2

Answer 2

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• refer attachment

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hope it helps