If cos A + cos2 A = 1 then (sin2 A + sin4 A) = ?
Question:

If $\cos A+\cos ^{2} A=1$ then $\left(\sin ^{2} A+\sin ^{4} A\right)=?$

(a) $\frac{1}{2}$

(b) 2

(c) 1

(d) 4

 

Solution:

Given : $\cos A+\cos ^{2} A=1$

$\cos A+\cos ^{2} A=1$

$\Rightarrow \cos A=1-\cos ^{2} A$

$\Rightarrow \cos A=\sin ^{2} A \quad\left(\because \sin ^{2} A+\cos ^{2} A=1\right)$

Now,

$\sin ^{2} A+\sin ^{4} A=\sin ^{2} A+\left(\sin ^{2} A\right)^{2}$

$=\cos A+(\cos A)^{2}$

$=\cos A+\cos ^{2} A$

$=1$

Hence, the correct option is (c).

 

Administrator

Leave a comment

Please enter comment.
Please enter your name.