Trigonometric Identities

Hello Readers,

In this post we are sharing some c which are useful for SSC, Railways and other exams.

Pythagorean Identities:

  • sin2 ɸ + cos2 ɸ = 1
  • 1 + tan2 ɸ = sec2 ɸ
  • 1 + cot2 ɸ = cosec2 ɸ

Reciprocal Identities:

  • sin ɸ = 1/cosec ɸ
  • cos ɸ = 1/sec ɸ
  • tan ɸ = 1/cot ɸ

Ratio Identities:

  • tan ɸ = sin ɸ/cos ɸ
  • cot ɸ = cos ɸ/sin ɸ

Even/Odd Identities:

  • sin (-ɸ) = – sin ɸ                     cosec (-ɸ) = – cosec ɸ
  • cos (-ɸ) = cos ɸ                       sec (-ɸ) = sec ɸ
  • tan (-ɸ) = – tan ɸ                    cot (-ɸ) = – cot ɸ

Cofunction Identities:

  • sin (90-ɸ) = cos ɸ                   cos (90-ɸ) = sin ɸ
  • tan (90-ɸ) = cot ɸ                   cot (90-ɸ) = tan ɸ
  • sec (90-ɸ) = cosec ɸ               cosec (90-ɸ) = sec ɸ
  • sin (90+ɸ) = cos ɸ                   cos (90+ɸ) = – sin ɸ
  • tan (90+ɸ) = – cot ɸ                cot (90+ɸ) = – tan ɸ
  • sec (90+ɸ) = – cosec ɸ             cosec (90+ɸ) = sec ɸ

Values of some Trigonometric Functions:

table_trig

Click here to read: How to find Minimum and Maximum values of Trigonometric Functions