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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.

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Date:___________________

High School Mathematics - 2
10.12 Trignometry Identities

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

Q 2: Prove that (1+tanx)2 + (1-tanx)2 = 2 sec2x.
Answer:

Q 3: Prove that cos x/(sec x - tan x) = 1 + sin x
Answer:

Q 4: If cos x + sin x = 21/2 cos x, prove that cos x - sin x = 21/2 sin x.
Answer:

Q 5: Prove that sec4x = sec2x = tan2x + tan4
Answer:

Q 6: Prove that sin y/(1+cosy) + (1+cos y)/sin y = 2 cosec y
Answer:

Q 7: If tan x + sin x = m and tan x - sin x = n, show that m2 - n2 = 4mn1/2
Answer:

Q 8: If sin x + cosec x = 2, prove htat sin2 + cosec 2 = 2.
Answer:

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Question 10: This question is available to subscribers only!


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