MyQuestionIcon

1

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Sin(A+B)Sin(A-B)

Prove that: t...

Question

Prove that: $\tan 3 A \tan 2 A \tan A = \tan 3 A - \tan 2 A - \tan A$

Open in App

Solution

Determine the proof of the given expression $\tan 3 A \tan 2 A \tan A = \tan 3 A - \tan 2 A - \tan A$
Solve the L.H.S part:
Since we know that $3 A = 2 A + A . . . . . . . . . . . . . . . . . . . . . . . . . . . . (i)$
taking the $\tan$ both sides of the above equation.
$\tan 3 A = \tan (2 A + A) \Rightarrow \tan 3 A = \frac{\tan 2 A + \tan A}{(1 - \tan 2 A . \tan A)} \Rightarrow \tan 3 A (1 - \tan 2 A \tan A) = \tan 2 A + \tan A \Rightarrow \tan 3 A - \tan 3 A \tan 2 A \tan A = \tan 2 A + \tan A \Rightarrow \tan 3 A - \tan 2 A - \tan A = \tan 3 A \tan 2 A \tan A$
Hence, the L.H.S = R.H.S.

Suggest Corrections

thumbs-up

149

Similar questions

Q. Prove that :

|\begin{matrix} (a + 1) (a + 2) & a + 2 & 1 \\ (a + 2) (a + 3) & a + 3 & 1 \\ (a + 3) (a + 4) & a + 4 & 1 \end{matrix}| = - 2

Q. Prove that :

\frac{{tan}^{3} A - {cot}^{3} A}{tan A - cot A} = {sec}^{2} A + {cot}^{2} A .

Q. Solve this:
Question 16
Prove that
(i) tan 3A tan 2A tan A = tan 3A - tan 2A - tan A
(ii) cot A cot 2A - cot 2A cot 3A - cot 3A cot A = 1

tan 3 A - tan 2 A - tan A = tan A tan 2 A tan 3 A

c o t A c o t 2 A + c o t 2 A c o t 3 A + 2 = c o t A (c o t A - c o t 3 A)

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

Transformations

MATHEMATICS

Watch in App

explore_more_icon

Explore more

Sin(A+B)Sin(A-B)

Standard XII Mathematics

Join BYJU'S Learning Program

CrossIcon