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High School Mathematics - 2
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.