Question

prove that tan7A.tan4A.tan3A=tan7A-tan4A-tan3A ​

Answer 1

Answer:

To prove:-

tan7A.tan4A.tan3A=tan7A-tan4A-tan3A

Proof:-

As we know that

$\boxed {\sf 7A=4A+3A}$

$\\\qquad\quad\displaystyle\sf{:}\implies tan7A=tan (4A+3A)$

$\\\qquad\quad\displaystyle\sf{:}\implies tan7A=\dfrac {tan4A+tan3A}{1-tan4A.tan3A}$

• using cross multiplication method

$\\\qquad\quad\displaystyle\sf{:}\implies tan7A (1-tan4A.tan3A)=tan4A+tan3A$

$\\\qquad\quad\displaystyle\sf{:}\implies tan7A-tan7A.tan4A.tan3A=tan4A+tan3A$

$\\\qquad\quad\displaystyle\sf{:}\implies tan7A-tan4A-tan3A=tan7A.tan4A.tan3A$

$\\\qquad\quad\displaystyle\sf{:}\boxed {\sf {\implies tan7A.tan4A.tan3A=tan7A-tan4A-tan3A}}\qquad\qquad (Proved)$