Question

if cosQ+cos²Q=1 find the value of sin²Q+sin⁴Q​

Answer 1

${\bold{\underline{\underline{Answer:}}}}$

${\bold{\therefore {sin}^{2} Q + {sin}^{4} Q = 1}}$

${\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\underline \bold{given : } \\ \implies cos Q + { cos }^{2} Q= 1 \\ \\ \underline \bold{to \: find : } \\ \implies {sin}^{2} Q+ {sin}^{4} Q = ?$

• According to given question :

$\implies cosQ+ {cos}^{2} Q = 1 \\ \\ \implies cosQ = 1 - {cos}^{2} Q \\ \\ \bold{\implies cos Q = {sin}^{2} Q} - - - - - (1) \\ \\ \bold{For \: finding \: value : } \\ \implies {sin}^{2} Q + {sin}^{4} Q \\ \\ \implies {sin}^{2} Q+ ( {sin}^{2} Q)^{2} \\ \\ \implies cosQ + {cos}^{2} Q \\ \\ \bold{\implies 1} \: \: \: \bold{(given)} \\ \\ \bold{\therefore {sin}^{2} Q + {sin}^{4} Q = 1}$