Flashcards
Trigonometry
[Show more]
Preview 5 out of 10 Flashcards
Prove that:
(1 - sin A)/(1 + sin A) = (sec A - tan A)2
Prove that:
(1 - sin A)...
Solution:
L.H.S = (1 - sin A)/(1 + sin A)
= (1 - sin A)2/(1 - sin A) (1 + sin A),[Multiply both numerator and denominator by (1 - sin A)
(1 - sin A)2/(1 - sin2 A)
= (1 - sin A)2/(cos2 A), [Since sin2 θ + cos2 θ = 1 ⇒ cos2 θ = 1 - sin2 θ]
= {(1 - sin A)/cos A}2
= (1/cos A - sin A/cos A)2
= (sec A – tan A)2 = R.H.S. Proved.
tan4 θ + tan2 θ = sec4 θ - sec2 θ
tan4 θ + tan2 θ = sec4 θ - sec2 θ
L.H.S = tan4 θ + tan2 θ
= tan2 θ (tan2 θ + 1)
= (sec2 θ - 1) (tan2 θ + 1) [since, tan2 θ = sec2 θ – 1]
= (sec2 θ - 1) sec2 θ [since, tan2 θ + 1 = sec2 θ]
= sec4 θ - sec2 θ = R.H.S. Proved.
cos θ/(1 - tan θ) + sin θ/(1 - cot θ) = sin θ + cos θ
cos θ/(1 - tan θ) + sin θ/(1 - cot θ) = sin θ + cos θ
Solution:
L.H.S = cos θ/(1 - tan θ) + sin θ/(1 - cot θ)
= cos θ/{1 - (sin θ/cos θ)} + sin θ/{1 - (cos θ/sin θ)}
= cos θ/{(cos θ - sin θ)/cos θ} + sin θ/{(sin θ - cos θ/sin θ)}
= cos2 θ/(cos θ - sin θ) + sin2 θ/(cos θ - sin θ)
= (cos2 θ - sin2 θ)/(cos θ - sin θ)
= [(cos θ + sin θ)(cos θ - sin θ)]/(cos θ - sin θ)
= (cos θ + sin θ) = R.H.S. Proved.
Trigonometric identities:
cos2A + sin2A = 1
1 + tan2A = sec2A
cot2A + 1 = cosec2A
Trigonometric identities:
cos2A + sin2A = 1
1 + tan2A = sec2A
cot2A + 1 = cosec2A
Trigonometric ratios of complementary angles:
sin (90° – A) = cos A
cos (90° – A) = sin A
tan (90° – A) = cot A
cot (90° – A) = tan A
sec (90° – A) = cosec A
cosec (90° – A) = sec A
Prove that (sin4θ – cos4θ +1) cosec2θ = 2
Prove that (sin4θ – cos4θ +1) cosec2θ = 2
Solution:
L.H.S. = (sin4θ – cos4θ +1) cosec2θ
= [(sin2θ – cos2θ) (sin2θ + cos2θ) + 1] cosec2θ
Using the identity sin2A + cos2A = 1,
= (sin2θ – cos2θ + 1) cosec2θ
= [sin2θ – (1 – sin2θ) + 1] cosec2θ
= 2 sin2θ cosec2θ
= 2 sin2θ (1/sin2θ)
= 2
= RHS
Flip
Seller
Follow
outofhome
Reviews received
The benefits of buying summaries with Stuvia:
Created by fellow students, verified by reviews
Quality you can trust: written by students who passed their tests and reviewed by others who've used these notes.
Didn't get what you expected? Choose another document
No worries! You can instantly pick a different document that better fits what you're looking for.
Pay as you like, start learning right away
No subscription, no commitments. Pay the way you're used to via credit card and download your PDF document instantly.
Frequently asked questions
What do I get when I buy this document?
You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.
Satisfaction guarantee: how does it work?
Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.
Who am I buying these notes from?
Stuvia is a marketplace, so you are not buying this document from us, but from seller outofhome. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy these notes for $15.99. You're not tied to anything after your purchase.
Can Stuvia be trusted?
4.6 stars on Google & Trustpilot (+1000 reviews)
46387 documents were sold in the last 30 days
Founded in 2010, the go-to place to buy study notes for 16 years now
Recently viewed by you
Exam (elaborations) ·
Cisco CCNA Commands Cheat Sheet PDF – Complete CLI Study Guide for Exam Preparation
Other ·
IDRL 308 UNIT 2 DEFINITIONS STUDY GUIDE
Package deal ·
ALLES EXAM BUNDLE SET 2024
Exam (elaborations) ·
NFHS
Package deal ·
Eduqas A Level English Language Component 2 Bundle
Other ·
NR446 Exam 1 Study Guide
Exam (elaborations) ·
Advanced Practice Nursing
Summary ·
Problemáticas ambientales
