Question

cos^4 theta-cos^2 theta=sin^4 theta-sin^2 theta

Answer 1

Answer:

Hence it proved.

Step-by-step explanation:

To solve this you should know about all the formulas of trigonometry.

$important \: \: points = >$

check weather if any formula is formed by changing the place of values.

in above question it can be seen that ,

by changing the place the formula is formed.

${cos}^{4} \alpha - {cos}^{2} \alpha = {sin}^{4} \alpha - {sin}^{2} \alpha$

$take \: common \\ = > {cos}^{2} \alpha ( {cos}^{2} \alpha - 1) = {sin}^{2} \alpha ( {sin}^{2} \alpha - 1)$

$= > \frac{ {cos}^{2} \alpha }{ {sin}^{2} \alpha }( {sin}^{2} \alpha) = ( {cos}^{2} \alpha )$

because ,

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

$= > \frac{ {cos}^{2} \alpha }{ {sin}^{2} \alpha } = \frac{ {cos}^{2} \alpha }{ {sin}^{2} \alpha }$

$= > {cot}^{2} \alpha = {cot}^{2} \alpha$

hence It proved

mark it brainliest ☺️

❤️AR+NAV❤️