Sponsor Area

Inverse Trigonometric Functions

Question
CBSEENMA12036223

If cos-1 x - cos-1 y/2 = α, then 4x2 − 4xy cos α + y2 is equal to

  • 2 sin 2α

  • 4

  • 4 sin2 α

  • − 4 sin2 α

Solution

C.

4 sin2 α

cos to the power of negative 1 end exponent space straight x space minus space cos to the power of negative 1 end exponent space straight y over 2 space equals straight alpha
cos to the power of negative 1 end exponent space open parentheses xy over 2 plus square root of left parenthesis 1 minus straight x squared right parenthesis open parentheses 1 minus straight y squared over 4 close parentheses end root close parentheses space equals space straight alpha
cos to the power of negative 1 end exponent space open parentheses fraction numerator xy space plus space square root of 4 minus straight y squared minus 4 straight x squared plus straight x squared straight y squared end root over denominator 2 end fraction close parentheses space equals space straight alpha
rightwards double arrow 4 minus straight y squared minus 4 straight x squared space plus straight x squared straight y squared space equals space 4 space cos squared space straight alpha space plus space straight x squared straight y squared minus 4 xy space cos space straight alpha
rightwards double arrow space 4 minus straight y squared minus 4 straight x squared space plus straight x squared straight y squared space equals space 4 space cos squared straight alpha space plus straight x squared straight y squared minus 4 xy space cos space straight alpha
rightwards double arrow space 4 straight x squared plus straight y squared minus 4 xy space cos space straight alpha space equals space 4 space sin squared space straight alpha

Sponsor Area

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