Math, asked by saaysaurabh42, 1 year ago

Find the value of tan1 tan2 tan3........tan88 tan89

Answers

Answered by AnanyaSrivastava999
4
tan 1 tan2 tan 3 tan4 .....tan 89
we know that
tan (90-x)= cot x
also cot x = 1/tan x
=> cot x × tan x = 1
so we have
tan1 = tan (90-89) = cot 89
similarly
tan 2= tan (90-88) = cot 88

now we can say that
tan 1 tan2 tan 3 tan4 .....tan 89
= tan 45
= 1

Answered by Anonymous
10
 <b> <I>

Hey there !!

▶ Find the value of :-)

→ tan 1° tan 2° tan 3° ...... tan 88° tan 89°.

= tan 1° tan 2°...... tan 44° tan 45° tan 46° ...... tan 88° tan 89°.

= ( tan 1°•tan 89° ) ( tan 2°•tan 88° ) .... ( tan 44°•tan46° ) • tan 45°.

= { tan 1°•tan( 90°-1° )}•{ tan 2°•tan(90°-2° ) }.... { tan 44°•tan(90°-44° )} • tan 45°.

= ( tan 1°•cot 1° )( tan 2°•cot 2° ) .... ( tan 44°•cot 44° ) • 1.

 \bf{ [ => tan ( 90° - \theta ) = cot \theta \: and \:  tan 45° = 1. ] }

= 1 × 1 × ..... × 1 × 1 .

 \bf{ [ tan \theta × cot \theta = 1 ] }

 \huge \bf \boxed{= 1.}

✔✔ Hence, it is solved ✅✅.

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 \huge \bf{ \# \mathbb{B}e \mathbb{B}rainly.}

BlackVenom05: Nicely written...
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