Question

tan^2thetacos^2theta = 1-cos^2theta​

Answer 1

♀ Question ♀

Prove that

${tan}^{2}θ \: {cos}^{2} θ = 1 - {cos}^{2} θ.$

♀ Solution ♀

LHS =

${tan}^{2}θ \: {cos}^{2} θ</p><p>$ [/tex]

= \frac{ {sin}^{2 \: θ } }{ {cos}^{2 \: θ} } \times {cos}^{2} θ [/tex]

$</p><p>= {sin}^{2} θ$

$</p><p>= 1 - {cos}^{2} θ$

= RHS

Hence Proved!

${\small \orange{\bigstar{ \small{ \underline{ \underline{ \underline{ \bold { \color{aqua}{And \: We \: Are \: Done :-}}}}}}}}}$

Answer 2

Step-by-step explanation:

L.H.S

Tan^2theta×cos^2theta

=sin^2theta/cos^2theta×cos^2theta (tan theta= sin theta/ cos theta)

=sin^2theta

R.H.S

1-Cos^2theta

=sin^2theta

L.H.S=R.H.S

Hence proved