All types of list of trigonometric identities
We can categorize trig identities in many form, Below is a list of trigonometric identities,
Pythagoras trigonometric identities
sin2x + cos2x = 1
1 + tan2x = sec2x
1 + cot2x = cosec2x
Reciprocal trigonometry identities
sinA = 1 / cosecA
cosA = 1 / secA
tanA = 1 / cotA
Quotient trig identities
tanA = sinA / cosA
cotA = cosA / sinA
double angle trig identities
sin2A = 2sinAcosA
cos2A = cos2A – sin2A = 2cos2A – 1 = 1 – 2sin2A
tan2A = 2tanA / (1 – tan2A)
Half angle identities
Complex Trigonometric Identities
Inverse trigonometric identities
- sin-1x + cos-1x = π / 2
- tan-1x + cot-1x = π / 2
- sec-1x + cosec-1x = π / 2
All above fundamental trigonometric identities can be identified as trigonometric identities table. Now let us enhance our knowledge by proving trigonometric identities. Here is a trigonometric identities proof for some of trig identities.
By using Pythagoras theorem in above right-angle triangle ABC,
AC2 = AB2 + BC2 -------------- (1)
=> 1 = (AB2 / AC2) + (BC2 / AC2)
=> 1 = sin2C + cos2C (as, sinC = AB/AC and cosC = BC/AC)
=> sin2C + cos2C = 1
for second trigonometric identity divide equation (1) by AB2,
so, (AC2 / AB2) = (AB2 / AB2) + (BC2 / AB2)
=> (AC2 / AB2) = 1 + (BC2 / AB2)
=> cosec2C = 1 + cot2C
=> 1 + cot2C = cosec2C
for third divide equation (1) by BC2,
so, (AC2 / BC2) = (AB2 / BC2) + (BC2 / BC2)
=> (AC2 / BC2) = (AB2 / BC2) + 1
=> sec2C = tan2C + 1
=> tan2C + 1 = sec2C
In the next section we will see procedure for verifying trigonometric identities.
Process of verifying trig identities
Currently you might have a question how to verify trigonometric identities? Let us see procedure for verifying trig identities by example.
Now we will see difference between trigonometric identities and equations. Trigonometric identities help us to change one trig function to another where as in case of equations we have to find values of angles which makes trig statement true. Let's have a example for that,
Up till now we have finished almost all trigonometric identities, now its time to find out how to solve trigonometric identities. But before solving trigonometric identities we will first see derivatives of trigonometric functions.
All above identities will help you to solve trigonometric identities problems, let us check how.
San Francisco, USA
"If you're at school or you just deal with mathematics, you need to use Studygeek.org. This thing is really helpful."
"I will recommend Studygeek to students, who have some chalenges in mathematics. This Site has bunch of great lessons and examples. "
" I'm a geek, and I love this website. It really helped me during my math classes. Check it out) "
"I use Studygeek.org a lot on a daily basis, helping my son with his geometry classes. Also, it has very cool math solver, which makes study process pretty fun"