Find the value of ( tan &#x2061;<!-- ⁡ --> 35 <mrow class="MJX-TeXAtom-ORD"> &#

patzeriap0

patzeriap0

Answered question

2022-05-31

Find the value of ( tan 35 ° + tan 55 ° ) ( sin 35 ° + sin 55 ° + 1 ) ( cos 35 ° + cos 55 ° + 1 )

Answer & Explanation

Melina Glover

Melina Glover

Beginner2022-06-01Added 11 answers

Let a = 35 ° . Then,
( tan 35 ° + tan 55 ° ) ( sin 35 ° + sin 55 ° + 1 ) ( cos 35 ° + cos 55 ° + 1 ) = tan 2 a + 1 tan a ( sin a + cos a + 1 ) 2 = 1 sin a cos a 2 ( 1 + sin a cos a + sin a + cos a ) = 2 ( 1 + sin a ) ( 1 + cos a ) sin a cos a = 2 cos a 1 sin a 1 + cos a sin a = 2 sin ( 90 a ) 2 sin 2 ( 45 a 2 ) 2 cos 2 a 2 2 sin a 2 cos a 2 = 2 cos ( 45 a 2 ) cos a 2 sin ( 45 a 2 ) sin a 2 = 2 cot 55 2 cot 35 2

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