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TYPE III

Example 1 Prove that

Solution

...Identity to be verified.

Example 2 Verify that cos a + sin a tan a = sec a

Solution

cos a + sin a tan a = sec a     ...identify to be verified.

Example 3 Prove that cot + tan = cosec sec

Solution

Example 4 sin4 A - cos4 A = 1- 2 cos2A Prove this!

Solution

sin 4 A - cos4A = 1 - 2cos2 A ....identity to be verified.

(sin2 A - cos 2A) (sin 2 A + cos2A) = 1 - 2cos2 A ...factorizing.

(sin2 A - cos2A) 1 = 1 - 2 cos 2A ....Pythagorean relation.

1- cos2 A - cos 2A = 1- 2 cos 2A .....Pythagorean relation,    sin2A= 1-    cos2 A

\ 1 - 2 cos2 A = 1 -2 cos2A .... algebric manipulation.

Example 5

Solution

Example 6 Prove tan2 - sin2 = tan2 sin2

Solution

Example 7 = csc + cot Prove.

Solution

Note : reasoning is left to you.

Example 10

Solution

Example 9 Verify that

Solution

Example 10

Solution

\ tan A. tan B = tan A tan B

Example 11

Prove this !

Solution

To prove this identity, it is advisable to rearrange the terms, then the example is, to prove 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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