Question

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

(a) -1

(b) 0

(c) 1

(d) 2​

Answer 1

Answer:

They have given cosθ + cos²θ = 1

so cosθ = 1 - cos²θ

so cosθ = sin²θ      (∵ sin²θ + cos²θ = 1)

so in the equation sin² θ + sin⁴θ

we can replace as cos θ + cos²θ   (∵ cos θ = sin²θ )

so the answer is 1

so the correct option is c) 1

Step-by-step explanation:

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Answer 2

SOLUTION

GIVEN

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

TO CHOOSE THE CORRECT OPTION

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

(a) - 1

(b) 0

(c) 1

(d) 2

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

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

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

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

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

$\sf{ = 1 }$

FINAL ANSWER

Hence the correct option is (c) 1

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