Q.

If  tan11+x21x21+x2+1x2=α, then  x2 is equal to

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a

cos2α

b

sinα

c

cosα

d

sin2α

answer is A.

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Detailed Solution

The given equation can be written as  1+x21x21+x2+1x2=tanα=sinαcosα

21+x221x2=cosα+sinαcosαsinα

[Applying componendo and dividendo]

1+x21x2=1+sin2α1sin2α 

1x21+x2=1sin2α1+sin2α

Squaring on both sides

1x2+1+x21x21x2=1sin2α+1+sin2α1sin2α1sin2α

22x2=22sin2α

x2=sin2α.

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