Q. 154.4( 13 Votes )

# Show that tan^{4} θ +tan^{2} θ =sec^{4} θ -sec^{2} θ.

Answer :

L.H.S: tan^{4}θ + tan^{2} θ

Taking tan^{2} θ common, we get

tan^{2} θ (tan^{2} θ + 1)

= tan^{2} θ sec^{2} θ [∵ sec^{2} θ – tan^{2} θ = 1 ⇒ tan^{2} θ + 1 = sec^{2} θ]

= (sec^{2} θ – 1) sec^{2} θ [∵tan^{2} θ = sec^{2} θ – 1]

= sec^{4} θ – sec^{2} θ

: R.H.S

Rate this question :

How useful is this solution?

We strive to provide quality solutions. Please rate us to serve you better.

Related Videos

Goprep Genius Quiz | Redox Reactions and its Applications35 mins

Quiz | Applications of Trigonometry47 mins

Trigonometric Identities44 mins

NCERT | Imp. Qs. on Applications of Trigonometry54 mins

Champ Quiz | Trigonometry Important Questions33 mins

Solving NCERT Questions on Trigonometric Identities56 mins

NCERT I Trigonometric Ratios50 mins

Smart Revision | Revise Trigo Like an Expert51 mins

NCERT | Trigonometric Identities52 mins

NCERT | Discussion on Imp. Qs. of Trignometry45 mins

Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Expertsview all courses

Dedicated counsellor for each student

24X7 Doubt Resolution

Daily Report Card

Detailed Performance Evaluation

RELATED QUESTIONS :

Prove the following identities :

tan^{4}θ + tan^{2}θ = sec^{4}θ – sec^{2}θ

Prove the following identities :

sin^{2} θ(1+ cot^{2} θ) = 1

Prove the following identities :

cos^{2} A (tan^{2} A+1) = 1

If sin 77° = x, then write the value of cos 77^{o} in terms of x.

If cos55° = x^{2}, then write the value of sin 55^{o} in terms of x.

If cos40^{o} = p, then write the value of sin 40^{o} in terms of p.