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4.4 Tangent Identities

1) Sum and Difference Identities

Double (Multiple) angle and Half (sub multiple) angle Identities

EXAMPLE 1 Prove that tan 200 + tan 250+ tan 200 (tan 250) = 1

Solution :

EXAMPLE 2 Find tan 750

Solution:

EXAMPLE 3 Prove that tan 500= tan 400 + 2 tan 100

Solution:

\ tan 500 - tan 400 + 2 tan 100

EXAMPLE 4 If A + B = p /4, then prove that ( 1 + tan A ) (1 + tan B) = 2

Solution :

\ A + B = p/4 ie, 450

\ tan (A + B ) = tan ( 45 0 )

EXAMPLE 5 Evaluate

Solution :

EXAMPLE 6 If tan x = 5 / 6 and tan y = 1 / 11. Show that x + y = p / 4 rad.

Solution:

EXAMPLE 7 Find the value of tan (a + b) where a is in Quad III and b is in Quad .II such that cos a = -3/5 and sin b = 20/29.

Solution: Since cos a = -3/5

\ sin2a = 1 - cos2a

\ sin2 a= 1 -9/25 =16/25

\ sin a = -4/5, sine is negative in Quad III.

EXAMPLE 8 Using half -angle identity find tan 150

Solution:

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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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