The value of (cosA+cosBsinA−sinB)n+(sinA+sinBcosA−cosB)n is
A
2tannA−B2
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B
2cotnA−B2:niseven
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C
0:nisodd
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D
none
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Solution
The correct option is C0:nisodd (cosA+cosBsinA−sinB)n+(sinA+sinBcosA−cosB)n(2cosA+B2⋅cosA+B22cosA+B2⋅sinA+B2)n+(2sin(A+B2)⋅cos(A−B2)−2sinA+B2⋅sinA−B2)n[cotA−B2]n+[−cotA−B2]n