Question

Cos theta + cos2 theta =1 ,then sin2 theta +sin4theta =1.

Answer 1

cos2 theta+cos4 theta

=1-sin2 theta+cos2 theta*cos2theta

=sin theta+(1-sin2 theta)(1-sin2 theta)

=sin theta+sin theta*sin theta

=sin theta+sin2 theta

= 1

Answer 2

Given :

$\sf{ \cos \theta + { \cos}^{2} \theta = 1}$

To find :

To prove

$\sf{ { \sin}^{2} \theta +{ \sin}^{4} \theta } = 1$

Solution :

Here it is given that

$\sf{ \cos \theta + { \cos}^{2} \theta = 1}$

Now

$\sf{ \cos \theta + { \cos}^{2} \theta = 1}$

$\sf{ \implies \cos \theta = 1 - { \cos}^{2} \theta }$

$\sf{ \implies \cos \theta = { \sin}^{2} \theta }$

Now

$\sf{ { \sin}^{2} \theta +{ \sin}^{4} \theta }$

$\sf{ = { \sin}^{2} \theta + {({ \sin}^{2} \theta)}^{2} }$

$\sf{ = { \sin}^{2} \theta + {( \cos \theta)}^{2} }$

$\sf{ = { \sin}^{2} \theta + {\cos}^{2} \theta}$

$\sf{ = 1 }$

Hence proved

━━━━━━━━━━━━━━━━

Learn more from Brainly :-

$1.$ If cosθ+secθ=√2,find the value of cos²θ+sec²θ

https://brainly.in/question/25478419

2. Value of 3 + cot 80 cot 20/cot80+cot20 is equal to

https://brainly.in/question/17024513

3. In a triangle, prove that (b+c-a)(cotB/2+cotC/2)=2a×cotA/2

https://brainly.in/question/19793971