Question

If cose+cos²0=1,the value of sin²0+sin'e is option A- -1
B- 0
C- 1
D- 2​

Answer 1

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Answer 2

SOLUTION

CORRECT QUESTION

$\sf{ \cos \theta + { \cos}^{2} \theta = 1}$ the value of $\sf{ { \sin}^{2} \theta +{ \sin}^{4} \theta }$

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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