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### High School Mathematics - 210.12 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.
 Q 1: If tan x + sin x = m and tan x - sin x = n, show that m2 - n2 = 4mn1/2Answer: Q 2: Prove that (1+tanx)2 + (1-tanx)2 = 2 sec2x.Answer: Q 3: Prove that (1+cot x - cosec x)(1 +tan x + sec x) = 2Answer: Q 4: Prove that sec4x = sec2x = tan2x + tan4Answer: Question 5: This question is available to subscribers only! Question 6: This question is available to subscribers only!