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

sin^{2}x + cos^{2}x = 1

1 + tan^{2}x = sec^{2}x

1 + cot^{2}x = cosec^{2}x
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 = cos^{2}A – sin^{2}A = 2cos^{2}A – 1 = 1 – 2sin^{2}A

tan2A = 2tanA / (1 – tan^{2}A)
Half angle identities
Complex Trigonometric Identities
Inverse trigonometric identities
 sin^{1}x + cos^{1}x = π / 2
 tan^{1}x + cot^{1}x = π / 2
 sec^{1}x + cosec^{1}x = 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 rightangle triangle ABC,
AC^{2} = AB^{2 }+ BC^{2}  (1)
=> 1 = (AB^{2} / AC^{2}) + (BC^{2 }/ AC^{2})
=> 1 = sin^{2}C + cos^{2}C (as, sinC = AB/AC and cosC = BC/AC)
=> sin^{2}C + cos^{2}C = 1
for second trigonometric identity divide equation (1) by AB^{2},
so, (AC^{2 }/ AB^{2}) = (AB^{2} / AB^{2}) + (BC^{2} / AB^{2})
=> (AC^{2 }/ AB^{2}) = 1 + (BC^{2} / AB^{2})
=> cosec^{2}C = 1 + cot^{2}C
=> 1 + cot^{2}C = cosec^{2}C
for third divide equation (1) by BC^{2},
so, (AC^{2 }/ BC^{2}) = (AB^{2} / BC^{2}) + (BC^{2} / BC^{2})
=> (AC^{2 }/ BC^{2}) = (AB^{2} / BC^{2}) + 1
=> sec^{2}C = tan^{2}C + 1
=> tan^{2}C + 1 = sec^{2}C
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.
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