Question

$\text{If}\sin \theta +{\sin }^2\theta =1,\text{then}$
value of $1+{\cos }^4\theta +{\cos }^8\theta +2{\cos }^6\theta$ is equal to

• A. $1$
• B. $2$
• C. $3$
• D. $4$

Answer 1

The correct option is B $2$

Given,

$\text{If}\sin \theta +{\sin }^2\theta =1$

or, $\sin \theta =1-{\sin }^2\theta$

or, $\sin \theta ={\cos }^2\theta$ ........(1)

Now,

$1+{\cos }^4\theta +{\cos }^8\theta +2{\cos }^6\theta$

$=1+({\cos }^2\theta +{\cos }^4\theta {)}^2$

$=1+({\cos }^2\theta +{\sin }^2\theta {)}^2$ ..........[ Using (1)]

$=1+1^2$

$=2$.