Question

Evaluate:
cot 54 /tan 36 +tan 20 /cot 70 -2 tan 45

Answer 1

Hi ,

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Trigonometric Ratios of Complementary Angles:

        Two angles are said to be complementary if their sum 

equals 90° .

here we use ,

tan ( 90 - A ) = cot A

or 

cot ( 90 - A ) = tan A

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i ) cot 54 = cot ( 90 - 36 ) = tan 36 ------- ( 1 )

ii ) tan 20 = tan ( 90 - 70 ) = cot 20 ------( 2 )

iii ) tan 45 = 1   --------------------------------( 3 )

According to the problem ,

cot 54 / tan 36  + tan 20 / cot 70 - 2tan 45

= tan 36 / tan 36 + cot 70 / cot 70 - 2 × 1    [ from ( 1 ) , ( 2 ) and ( 3 ) ]

= 1 + 1 - 2

= 2 - 2 

= 0

I hope this helps you .

*****

Answer 2

heya!!!!!


♦cot 54 = cot(90-36)=tan 36

♦tan 20=tan(90-70)=cot 70

♦we know the value of tan45 is 1


by substituting these values in the given question, we get

♦cot 54 /tan 36 +tan 20 /cot 70 -2 tan 45

♦ tan 36/tan 36 +cot 70/cot 70 -2(1)

♦ 1+1-2

♦0

I hope this will help u ;)

♥dhathri123♥