Question

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Answer 1

Explanation:

Answer given in pic.....

Answer 2

Explanation:

QUESTION GIVEN :

if Tan A = p/(p + 1) , Tan B= 1/(2p + 1) , show that A + B = Π/ 4

GIVEN ;

Tan A = p / ( p + 1)

Tan B = p /( 2p + 1)

TO SHOW ;

A + B = Π/ 4

FORMULA TO USED :

TAN ( A + B) = (TAN A + TAN B)/ (1 -TAN A.TANB)

SOLUTION FOR QUESTION ;

={ p/(p + 1) + 1(2p+ 1) }/1-{p /(p+ 1) × ( 1 / ( 2p + 1)

= p( 2p + 1) +(p + 1)/ ( p + 1) ( 2p + 1)/ { (2p +1 ) ( p + 1) -p ) / { p + 1) ( 2p + 1)

=( 2p² + p + p + 1) / (2p² +2p + 1)

= 1

Hence,

Tan( A+ B) = 1

or, Tan ( A + B) = Tan45 °

Therefore , Tan ( A+B) = Π/4 proved