Question

If sin + cosec = 2, then the value of sin2016 + cosec2016, is -
(1) 1
(2) 2016
(3) 2
(4) 4032

Answer 1

Solution:

sin + cosec = 2,

if you replace [] by 90 degree then,

Sin[90°] + Cosec [90°]=1+1=2

So, sin 2016[90°] + cosec 2016[90°]=1+1=2

As 90 * 2016= odd multiple of 90° = 1

Answer 2

Answer:

(3) 2

Step-by-step explanation:

Here, the given equation,

$sin\theta + cosec \theta = 2$

$sin \theta + \frac{1}{sin \theta}=2$   ( Because, cosec A = 1/sin A )

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

$sin^2 \theta + 1 = 2 sin \theta$

Let, sin $\theta$ = x,

$x^2+1=2x$

$x^2-2x+1=0$

$(x-1)^2=0$

$x-1=0$

$x=1$

$\implies sin \theta = 1$

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

Hence,

$sin^{2016} \theta + cosec^{2016} \theta$

$=(1)^{2016}+(1)^{2016}=1+1=2$