Question

if cosq+cos²Q=1.prove that sin²Q+sin4Q=1​

Answer 1

Answer:

Here's your required answer

Answer 2

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

$\green{\underline \bold{Given : }} \\ :\implies cos Q + { cos }^{2} Q= 1 \\ \\ \red{\underline \bold{To \: Prove : }} \\ :\implies {sin}^{2} Q+ {sin}^{4} Q = 1$

• According to given question :

$:\implies cosQ+ {cos}^{2} Q = 1 \\ \\ :\implies cosQ = 1 - {cos}^{2} Q \\ \\ \bold{:\implies cos Q = {sin}^{2} Q} - - - - - (1) \\ \\ \text{PROOF : } \\ :\implies {sin}^{2} Q + {sin}^{4} Q \\ \\ :\implies {sin}^{2} Q+ ( {sin}^{2} Q)^{2} \\ \\ :\implies cosQ + {cos}^{2} Q \\ \\ \bold{:\implies 1} \: \: \: \bold{(given)} \\ \\ \bold{\therefore {sin}^{2} Q + {sin}^{4} Q = 1}\\\\\:\:\:\:\:\:\:\:\:\:\green{\text{Proved}}$