kwizNET Subscribers, please login to turn off the Ads!
Email us to get an instant 20% discount on highly effective K-12 Math & English kwizNET Programs!

Online Quiz (Worksheet A B C D)

Questions Per Quiz = 2 4 6 8 10

High School Mathematics - 2
10.12 Trignometry Identities

Consider any acute angle AOB. P is a point on the ray OB and PQ is perpendicular to OA.

We have Sin = PQ/OP
Cos = OQ/OP
Tan = PQ/OQ
Cosec = 1/Sin = OP/PQ
Sec = 1/Cos = OP/OQ
Cot = 1/tan = OQ/OP

Important identities :
sin2 + cos2 = 1
1 + tan2 = sec2
1 + cot2 = cosec2

Example:
Show that cot + tan = sec.cosec
cot + tan = cos/sin + sin/cos
= cos2+sin2/sincos
= 1/sincos = 1/sin . 1/cos = cosec.sec





Directions: Find the mid point of the segment joining two points and draw a graph for the problems.
Q 1: If cos x + sin x = 21/2 cos x, prove that cos x - sin x = 21/2 sin x.
Answer:

Q 2: If sin x + cosec x = 2, prove htat sin2 + cosec 2 = 2.
Answer:

Q 3: Prove that (1+cot x - cosec x)(1 +tan x + sec x) = 2
Answer:

Q 4: Prove that tan x + cot x = sec x. cosec x
Answer:

Q 5: Prove that cos x/(sec x - tan x) = 1 + sin x
Answer:

Q 6: Prove that sec4x = sec2x = tan2x + tan4
Answer:

Q 7: Prove that sin y/(1+cosy) + (1+cos y)/sin y = 2 cosec y
Answer:

Q 8: If tan x + sin x = m and tan x - sin x = n, show that m2 - n2 = 4mn1/2
Answer:

Question 9: This question is available to subscribers only!

Question 10: This question is available to subscribers only!


Subscription to kwizNET Learning System offers the following benefits:

  • Unrestricted access to grade appropriate lessons, quizzes, & printable worksheets
  • Instant scoring of online quizzes
  • Progress tracking and award certificates to keep your student motivated
  • Unlimited practice with auto-generated 'WIZ MATH' quizzes
  • Child-friendly website with no advertisements
  • Choice of Math, English, Science, & Social Studies Curriculums
  • Excellent value for K-12 and ACT, SAT, & TOEFL Test Preparation
  • Get discount offers by sending an email to discounts@kwiznet.com

Quiz Timer