Skip to content
Exercises · Q8

Q.If sec⁡θ+tan⁡θ=5\sec\theta+\tan\theta=5, find the value of sec⁡θ−tan⁡θ\sec\theta-\tan\theta.

Puducherry TnboardTextbookSubjectiveImportance★★★★★est
8% · 3/36 Questions
🔒 Locked · start free trial →

You're viewing a preview — the full solution, concept, methods & PYQ mapping are locked.

Start your 14-day free trial to unlock the full solution →

Step 1 — recall the identity. 1+tan⁡2θ=sec⁡2θ⇒sec⁡2θ−tan⁡2θ=11+\tan^2\theta=\sec^2\theta \Rightarrow \sec^2\theta-\tan^2\theta=1.

Step 2 — factorise the left side as a difference of squares. sec⁡2θ−tan⁡2θ=(sec⁡θ+tan⁡θ)(sec⁡θ−tan⁡θ)\sec^2\theta-\tan^2\theta=(\sec\theta+\tan\theta)(\sec\theta-\tan\theta), so (sec⁡θ+tan⁡θ)(sec⁡θ−tan⁡θ)=1(\sec\theta+\tan\theta)(\sec\theta-\tan\theta)=1.

Step 3 — substitute the given value. 5×(sec⁡θ−tan⁡θ)=1⇒sec⁡θ−tan⁡θ=155\times(\sec\theta-\tan\theta)=1 \Rightarrow \sec\theta-\tan\theta=\dfrac15. …

Start your 14-day free trial to unlock the full solution →

Unlock everything free for 14 days

  • Full step-by-step solutions
  • Concept-first explanations
  • Methods, shortcuts & mistakes
  • PYQ mapping + timed mock tests
Start 14-day free trial →See Plans & Pricing →

Full access for 14 days. No credit card required.

←Previous questionQ5 — Determine the sign of cos200^° and tan320^°, without using a calculato…→Next questionQ10 — Find the value of cos15^° using the compound angle formula.