Question

plz answer this question ​

Answer 1

Step-by-step explanation:

★Given -

• ${ \rm{ \bf{{tan}^{2} \theta + {tan}^{4} \theta} }}$

★To prove -

• $\rm{ \bf{ {sec}^{4} \theta - {sec}^{2} \theta}}$

★Concept -

• Here, we'll manipulate the identity sec²∅ = 1 + tan²∅ to get the desired answer. Let's do it!

★Solution -

L.H.S

$\longmapsto{ \rm{ \bf{{tan}^{2} \theta + {tan}^{4} \theta} }}$

$\longmapsto{ \rm{ \bf{{tan}^{2} \theta(1 + {tan}^{2} \theta}) }}$

$\longmapsto{ \rm{ \bf{{tan}^{2} \theta( {sec}^{2} \theta}) }}$

∵ sec²∅ = 1 + tan²∅

$\longmapsto{ \rm{ \bf{({sec}^{2} \theta - 1)( {sec}^{2} \theta}) }}$

∵ sec²∅ = 1 + tan²∅

=> sec²∅ - 1 = tan²∅

$\longmapsto{ \rm{ \pink{ \bf{{sec}^{4} \theta - sec}^{2} \theta }} \pink= \pink{\rm R.H.S}}$

★More to know -

• $\rm{ \bf{sin}^{2} \theta + {cos}^{2} \theta = 1}$
• $\rm{ \bf {sec}^{2} \theta = 1 + {tan}^{2} \theta}$
• $\rm{ \bf {cosec}^{2} \theta = 1 + {cot}^{2} \theta}$

Answer 2

Step-by-step explanation:

$\longmapsto{ \rm{ \bf{({tan}^{2} \theta - 1)( {sec}^{2} \theta}) }}$

$\longmapsto{ \rm{ \bf{({sec}^{2} \theta - 1)( {sec}^{2} \theta}) }}$

$\longmapsto{ \rm{ \pink{ \bf{{sec}^{4} \theta - sec}^{2} \theta }} \pink= \pink{\rm R.H.S}}$