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Prove that Cos20-sin20/cos20+sin20=tan25

Prove that
Cos20-sin20/cos20+sin20=tan25

Grade:11

1 Answers

Abhishek Doyal
askIITians Faculty 25 Points
7 years ago
cos20-sin20/cos20+sin20
take cos 20 common from numerator and denominator
cos20(1-sin20/cos20)/cos20(1+sin20/cos20)
then cos20 and cos 20 cancelled form numerator and denominator and sin20/cos20=tan20

now remaining part will be
1-tan20/1+tan20 eq 1
one should be written as 1=tan 45 eq2

by eq 1 and eq 2
=tan45-tan20/1-tan45.tan20 eq 3

because tan(A-B)=tanA-tanB/1-tanA.tanB eq 4
by eq 4
eq 3=tan (45-20)= tan25

Abhishek doyal
Askiitian tutor
IIT Bombay

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