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Example 3 If cot a = 3 and p < a < 3p /2 . Find 4 sin a + 2 cos a

Solution :

p < a < 3p /2 means a lies in IIIrd Quadrant.

\ sin a and cos a are negatives.

Example 4

if tan

Solution : since p < A < 3/2 p, A lies in the IIIrd Quardrant.

\ Both csc A and sec A are negative.

Example 5
5 tan Find the value of cosec A - sin B.

Solution :

Example 6 where A and B are angles in the second Quadrant.

Prove that 4 cos A+ 3 cos B = -5.

Solution : 1) We have is II Quadrant.

From cos2A = 1- sin2A we get

Example 7 If sin , determine the values of tan , sec , and csc .

Solution : We know that m2+ n2)2- (m2- n2)2 = 4 m 2 n2

Given that

observing the adjoining fig it follows that

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Index

Trignometric Identities

4.1 Fundamental Identities
4.2 The addition formulas
4.3 The multiple-angle (Double & Half angle) formulas
4.4 Tangent Identities
4.5 Factorization & Defactorization

Supplementary Problems


Chapter 5

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