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Question

cos−1(3+5cosx5+3cosx) is equal to

A
tan1(12tanx2)
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B
tan1(tanx2)
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C
12tan1(2tanx2)
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D
2tan1(12tanx2)
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Solution

The correct option is D 2tan1(12tanx2)
cosx=1tan2(x2)1+tan2(x2)
Substituting in the equation we get
cos1⎜ ⎜ ⎜ ⎜3+3tan2(x2)+55tan2(x2)5+5tan2(x2)+33tan2(x2)⎟ ⎟ ⎟ ⎟


=cos1⎜ ⎜ ⎜ ⎜82tan2(x2)8+2tan2(x2)⎟ ⎟ ⎟ ⎟

=cos1⎜ ⎜ ⎜ ⎜4tan2(x2)4+tan2(x2)⎟ ⎟ ⎟ ⎟

=cos1⎜ ⎜ ⎜ ⎜114tan2(x2)1+14tan2(x2)⎟ ⎟ ⎟ ⎟

=2tan1(12tan(x2))



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