Question

If
$cosa + {cos}^{2} a = 1$
then the value of
${sin}^{2} a + {sin}^{4} a$
is
(A) -1. (B) 0 (C) 1 (D) 2​

Answer 1

Step-by-step explanation:

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Answer 2

$\huge\star\frak{\underline{AnSwer:-}}$

ɢɪᴠᴇɴ :

$\star$ $\normalsize\sf \red{cosa + cos^2 = 1}$

ᴛᴏ ғɪɴᴅ :

$\star$ $\normalsize\sf \purple{sin^2a + sin^4a}$

sᴏʟᴜᴛɪᴏɴ:

$\normalsize\hookrightarrow\sf\ cosa + cos^2 = 1 \\ \\ \normalsize\hookrightarrow\sf\ cosa = 1- cos^2a$

$\scriptsize\sf{\: \: \: \: \: \:( \therefore\ \: \pink{ 1 -cos^2\theta = sin^2\theta}) }$

$\normalsize\sf\hookrightarrow\ cosa = sin^2a$

$\rule{100}2$

$\normalsize\sf\hookrightarrow\ sin^2a + sin^4a \\ \\ \normalsize\sf\hookrightarrow\ sin^2a(1+sin^4a)$

$\scriptsize\sf{\: \: \: \: \: \:( \therefore\ \: \pink{ put \: the \: value \: of \: sin^2a}) }$

$\normalsize\hookrightarrow\sf\ cosa(1+cosa) \\ \\ \normalsize\hookrightarrow\sf\ cosa + cos^2a=1 \\ \\ \normalsize\hookrightarrow\sf\ sin^2a + sin^4a = 1$

$\hookrightarrow{\underline{\boxed{\sf\orange{sin^2a + sin^4a = 1}}}}$

$\huge\star\frak{\underline{Some \: Important :-}}$

$\boxed{\begin{minipage}{6cm} Important Trigonometric identities :- \\ \\ \: \: 1)\sin^2\theta+\cos^2\theta=1 \\ \\ 2)\sin^2\theta= 1-\cos^2\theta \\ \\ 3)\cos^2\theta=1-\sin^2\theta \\ \\ 4)1+\cot^2\theta=\text{cosec}^2 \, \theta \\ \\5) \text{cosec}^2 \, \theta-\cot^2\theta =1 \\ \\ 6)\text{cosec}^2 \, \theta= 1+\cot^2\theta \\\ \\ 7)\sec^2\theta=1+\tan^2\theta \\ \\ 8)\sec^2\theta-\tan^2\thetha=1 \\ \\ 9)\tan^2\theta=\sec^2\theta-1 \end{minipage}}$