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 sin^{4 }
A  cos^{4 }A = 1 2 cos^{2}A Prove this!
Solution
sin^{ 4} A  cos^{4}A = 1  2cos^{2}
A ....identity to be verified.
(sin^{2} A  cos^{ 2}A) (sin^{
2 }A + cos^{2}A) = 1  2cos^{2 }A ...factorizing.
(sin^{2 }A  cos^{2}A) 1 = 1 
2 cos^{ }^{ 2}A ....Pythagorean relation.
1 cos^{2 }A  cos^{ 2}A = 1
2 cos^{ 2}A .....Pythagorean relation, sin^{2}A=
1 cos^{2} A
\ 1  2 cos^{2}
A = 1 2 cos^{2}A .... algebric manipulation.
Example 5
Solution
Example 6 Prove tan^{2 }
 sin^{2} =
tan^{2}
sin^{2}
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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