Question

If cosƟ+cos2Ɵ =1,the value of sin2Ɵ+sin4Ɵ is

(a) -1

(b) 0

(c) 1

(d) 2​

Answer 1

Step-by-step explanation:

how 1is answer !???????

Answer 2

The question should be $\[\cos \theta + {\cos ^2}\theta = 1\]$ then the value of $\[{\sin ^2}\theta + {\sin ^4}\theta \]$ is-

Given:

$\[\cos \theta + {\cos ^2}\theta = 1\]$

To find : $\[{\sin ^2}\theta + {\sin ^4}\theta \]$

Solution:

Know that, $\[{\sin ^2}\theta + {\cos ^2}\theta = 1\]$.

$\[\therefore 1 - {\cos ^2}\theta = {\sin ^2}\theta &$

Rearrange the equation $\[\cos \theta + {\cos ^2}\theta = 1\]$,

$\[ \Rightarrow \cos \theta = 1 - {\cos ^2}\theta \]$

Put, $\[1 - {\cos ^2}\theta = {\sin ^2}\theta \]$

$\[ \Rightarrow \cos \theta = {\sin ^2}\theta \]$

Now, $\[{\sin ^2}\theta = \cos \theta \]$ in $\[{\sin ^2}\theta + {\sin ^4}\theta \]$,

$\[\begin{array}{l} = {\sin ^2}\theta + {\left( {{{\sin }^2}\theta } \right)^2}\\ = \cos \theta + \left( {\cos {\theta ^2}} \right)\\ = \cos \theta + {\cos ^2}\theta \\ = 1\end{array}\]$

Hence, the value of $\[{\sin ^2}\theta + {\sin ^4}\theta = 1\]$