Question

prove that: tan 26 tan 23 tan 45 tan 67 tan 64 =1​

Answer 1

Answer:

tan 26 = tan (90-64) = cot 64

tan 23 = cot 67

$= \cot(64 ) \times \cot(67) \times \tan(45) \times \tan(67) \times \tan(64) \\ = \frac{ \tan(67) }{ \tan(67) } \times \frac{ \tan(64) }{ \tan(64) } \times \tan(45 ) \\ = 1 \:$

H.P.

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Answer 2

In mathematics , trigonometry is one of its branch that define the connection between measure of angles and side-lengths in a triangle.

Explanation:

To prove: tan 26° tan 23° tan 45° tan 67° tan 64° =1​

Consider L.H.S

tan 26° tan 23° tan 45° tan 67° tan 64°

= tan 26° tan 23° tan 45° cot(90°-67°) cot (90°-64°)  [∵ tan A = cot (90°-A) ]

= tan 26° tan 23° tan 45° cot 23° cot 26°

= tan 26° cot 26°tan 23°cot 23° tan 45°  

=(1)(1)(1)                                  [∵ tan 45° =1 and tan A cot A =1]

=1 = R.H.S.

Hence proved.

# Learn more :

Tan 48 tan 23 - tan 42 tan 67​

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