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Please solve: tan[ 2 tan -1 (1/5) – pi/4] cos[pi/3 + tan -1 (-2)]

Please solve:
 
  1. tan[ 2 tan-1(1/5) – pi/4]
  2. cos[pi/3 + tan-1(-2)]

Grade:12

1 Answers

Ravi
askIITians Faculty 69 Points
9 years ago
1.
Consider tan-11/5 as x
=tan(2x-pi/4)

Use tan(A-B) to simplify the expression.

tan2x= 2 tanx/(1-tan2x)

and tan(tan-1x)=x
Use the mentioned relations to find evaluate the expression.

2.
Consider tan-1(-2) as x
So, tanx=-2
tan(pi-x)=2
So, find the value of sin(pi-x) and cos(pi-x) using the relationtan(pi-x)=2/1
sin(pi-x) and cos(pi-x) are infact equal to sinx and -cos x using the concepts of unit circle which should give you the value of x in terms of sin-1 and cos-1 of some numerical values which are to be used further in evaluating the expression.
cos[pi/3 + tan-1(-2)] can be simplified with cos(A-B) identity.

Using the derived relations for x in terms of sin-1and cos-1will give you the answer to the question.

P.S. Please post one question per post.

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