Question

Evaluates cos² theta tan² theta + tan² theta sin² theta in terms of tan theta​

Answer 1

$Value \: of \: cos^{2} \theta tan^{2} \theta + tan^{2} \theta sin^{2} \theta$

$= tan^{2} \theta (cos^{2} \theta + sin^{2} \theta)$

$= tan^{2} \theta \times 1$

/*By Trigonometric Identity*/

$\boxed{\pink{ cos^{2} \theta + sin^{2} \theta= 1}}$

$= tan^{2} \theta$

Therefore.,

$\red{Value \: of \: cos^{2} \theta tan^{2} \theta + tan^{2} \theta sin^{2} \theta}\green { = tan^{2} \theta }$

•••♪

Answer 2

ANSWER ✔

$\large\underline\bold{GIVEN,}$

$\dashrightarrow Value \: of \: cos^{2} \theta tan^{2} \theta + tan^{2} \theta sin^{2} \theta$

✯.TO EVALUATE IN TERMS OF TAN ∅

✯IDENTITY IN USE,

$\large{\boxed{\bf{ \star\:\:cos\theta+sin\theta= 1 \:\: \star}}}$

$\implies \: cos^{2} \theta tan^{2} \theta + tan^{2} \theta sin^{2}$

$\implies tan^2 \theta \bigg( cos^2 \theta +sin^2 \theta \bigg)$

$\implies tan^2 \theta \times 1 \:---\boxed{ from\:given\:identity.}$

$\implies tan^2\theta$

$\large{\boxed{\bf{ \star\:\: cos^{2} \theta tan^{2} \theta + tan^{2} \theta sin^{2} \theta= tan^2 \theta\:\: \star}}}$

HENCE DONE✔

_____________