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Question

Prove 2sin25π4+2cos27π4+2sec2π3=10

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Solution

2sin25π4+2cos27π4+2sec2π3

=2sin2(π+π4)+2cos2(2ππ4)+2(2)2

=2(sinπ4)2+2cos2π4+2(4)

=2(12)2+2(12)2+8

=1+1+8=10

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