Find the value of tan1 tan2 tan3........tan88 tan89
Answers
Answered by
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
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
10
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.
= 1 × 1 × ..... × 1 × 1 .
✔✔ Hence, it is solved ✅✅.
____________________________________
BlackVenom05:
Nicely written...
Similar questions