Page 7 - LN
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= [sin 2 + cos 2 + cosec 2 + 2 + sec 2 + 2]
= 1 + 2 + 2 + cosec 2 + sec 2 [since sin 2 + cos 2 = 1]
= 5 + cosec 2 + sec 2
= 5 + (1 + cot 2 ) + (1 + tan 2 )
[ 1 + cot 2 = cosec 2 and 1 + tan 2 = sec 2 ]
= 7 + cot 2 + tan 2
= RHS
Example8:If sec + tan = p, prove that
Solution: sec + tan = p
Squaring, we get,
(using cos 2 = 1- sin 2 ) (1 mark)
2
1 + sin = p (1 - sin )
2
2
p - p sin = 1 + sin
2
2
p - 1 = (p + 1)sin
Example 9:
Prove the following identity:
Given identity is
7
