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Please prove the following:
  1. 2cos-1 (3/root 13) + cot-1(16/63) + 1/2cos-1(7/25) = pi
  2. cos[2tan-1(1/7)] = sin[4tan-1(1/3)]

Harshitha Cheekala , 10 Years ago
Grade 12
anser 1 Answers
viswanath

Last Activity: 10 Years ago

   2cos-1(3/√13) +cot-1(16/63) +1/2cos-1(7/25)
=2tan-1(2/3) +tan-1(63/16) + 1/2tan-1(24/7)
=tan-1(12/5) + tan-1(63/16) + 1/2(2tan-1(3/4))
=tan-1(12/5) + tan-1(63/16) + tan-1(3/4)
= (tan-1(12/5) + tan-1(3/4)) + tan-1(63/16)
= (pi-tan-1(63/16)) +tan-1(63/16)
= pi
 
cos(2tan-1(1/7))= cos(tan-1(7/24))= cos(cos-1(24/25))=24/25
sin(4tan-1(1/3))=sin(2tan-1(3/4))=sin(tan-1(24/7))=sin(sin-1(24/25))=24/25

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