Question

if cos theta + cos square theta equals to 1 the value of sin square theta + sin raise the power 4 theta is
​

Answer 1

Answer:

1

Step-by-step explanation:

Given:

cos θ + cos² θ = 1

sin²θ + sin⁴θ =?

cos θ + cos² θ = 1

⇒ cos θ = 1 - cos² θ

⇒ cos θ = sin²θ (∵ sin²θ = 1 - cos² θ)

Now,

sin²θ + sin⁴θ

= sin²θ + (sin² θ)²

Substituting sin²θ = cos θ

cos θ + (cos θ)² = cos θ + cos² θ = 1

Answer 2

SOLUTION

GIVEN

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

TO DETERMINE

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

EVALUATION

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

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

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

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

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

$\sf{ = 1 }$

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