Question

ANSWER THIS FAST 2 questions

Answer 1

$\textbf{Answer(1)}$


$\textbf{Equation}$

${ \cos}^{4} a - { \sin}^{4} a + 1 = 2 { \cos }^{2} a$

$\textbf{Step(1)}$


Right first term in factories form

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


$\textbf{step2}$


Apply phythagorean identity


${ \cos }^{2} a + { \sin}^{2} a = 1$


Eq become


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

$\texbf{Step.3}$


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


$\textbf{Step 4}$


$\textbf{Using , identity}$


$1 - { \sin }^{2} a = { \cos }^{2} a$


On putting in above eq we, get

$= > { \cos }^{2} a + { \cos }^{2} a = 2 { \cos}^{2} a$



$\textbf{Step 5}$

$2 { \cos }^{2} = 2 { \cos }^{2}$

$\textbf{Hence}$


since,left hand side is equal to right bend side

so hence proved




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$\textbf{Answer 2}$


$\texbf{Equation}$


$\sin(a) + \cos(a) (1 - \sin(a) \cos(a) = { \sin }^{3} a+ { \cos}^{3} a$


Prove left hand side to equal the right hand side


$\textbf{Step.1}$



$\sin(a) + \cos(a) - { \sin}^{2} a \cos{a} - { \cos}^{2} a \sin(a)$



$\\textbf{Step2}$


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


$\textbf{Step 3}$

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

$\textbf{Step 4}$


$= { \sin}^{3} a + { \cos }^{3} a$

Answer 2

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