Question

If $sin\theta +cosec\theta =2,thensi{n}^6\theta +cose{c}^6\theta$ is equal to

• A. 0
• B. 2³
• C. 2
• D. 2⁶

Answer 1

The correct option is C

2

Given:
$sin\theta +cosec\theta =2$
$\Rightarrow sin\theta +\frac{1}{sin\theta }=2$
$\Rightarrow \frac{{sin}^2\theta +1}{sin\theta }=2$
$\Rightarrow {sin}^2\theta +1=2sin\theta$
$\Rightarrow {sin}^2\theta -2sin\theta +1=0$
$\Rightarrow (sin\theta -1{)}^2=0$
$\Rightarrow (sin\theta -1)=0$
$\Rightarrow sin\theta =1$
$\Rightarrow \theta ={90}^{\circ }$
$\Rightarrow cosec\theta =1$
$\Rightarrow si{n}^6\theta +cose{c}^6\theta =1^6+1^6$
$=1+1=2$