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Solution:We have,

2
o
2
o
4
o
4
o
o
2
Example 3: Prove that 2(cos 60 + sin 30 ) - (tan 60 + cot 45 ) + 3sec 30 = .

o
o
o
2
4
2
o
o
4
2
Solution:(cos 60 + sin 30 ) - (tan 60 + cot 45 ) + 3sec 30

Example 4 :If sin (A + B) = 1 and cos (A - B) =, then find A and B.
Solution :We have,
sin(A + B) = 1
o
sin(A + B) = sin 90
o
A + B = 90 (i)
Also, cos (A - B) =
o
cos(A - B) = cos 30
o
A - B = 30 (ii)

Adding (i) and (ii), we get,
o
o
A + B + A - B = 90 + 30
o
2A = 120
o
A = 60
o
Putting A = 60 in (i), we get,
o
o
60 + B = 90
o
B = 30
o
o
Hence, A = 60 and B = 30 .

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