Question

48. If cos A + cos²A = 1 then sin? A+ sinº A = ?
​

Answer 1

COS^2A=1-SIN^2A

THEREFORE

2[1-SIN^2A]=1

2-2SIN^2A=1

-2SIN^A=1-2

2SIN^A=1

SIN^2A=1/2

UNDERROOTON BOTH SIDE

SINA=1/ROOT2

SINA+SINA=1/ROOT2+1/ROOT2

SINA+SINA=2/ROOT2

SINA+SINA=ROOT2

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Answer 2

QUESTION:

If

$\cos(a) + { \cos(a) }^{2} = 1$

then

$\sin {a}^{2} + { \sin(a) }^{4} = ......$

(correct question )

☆ANSWER:

We use the trigonometry identity here ;

$\huge\pink { { \sin( \alpha ) }^{2} + { \cos( \alpha ) }^{2} = 1}$

with this identity we can say that,

${ \sin( \alpha ) }^{2} = 1 - { \cos( \alpha ) }^{2}$

or

${ \cos( \alpha ) }^{2} = 1 - { \sin( \alpha ) }^{2}$

now come to main question ;

$\cos(a) + { \cos(a) }^{2} = 1$

$\cos(a) = 1 - { \cos(a) }^{2}$

so,

$\cos(a) = { \sin(a) }^{2} \\ (with \: identity)$

such that;

$\cos(a) = { \sin(a) }^{2}$

so,

${ \cos(a) }^{2} = { \sin(a) }^{4}$

now,

$\huge\blue {{ \sin(a) }^{2} + { \sin(a) }^{4} = 1}$

☆other trigonometry identity;

1.

$1 + { \tan( \alpha ) }^{2} = { \sec( \alpha ) }^{2}$

2.

$1 + { \cot( \alpha ) }^{2} = { \csc( \alpha ) }^{2}$

3.

$\tan( \alpha ) \times \cot( \alpha ) = 1$