Question

prove that cot (10°-1)(cot35°-1)=2​

Answer 1

Answer:

To prove:-

cot (10°-1)(cot35°-1)=2

Proof:-

We know that

$\boxed{\sf 10°+35°=45°}$

$\\\qquad\quad\displaystyle\sf{:}\implies cot (10°+35°)=cot45°$

$\\\qquad\quad\displaystyle\sf{:}\implies \dfrac {cot10°.cot35°-1}{cot35°+cot10°}=1$

$\\\qquad\quad\displaystyle\sf{:}\implies cot10°.cot35°-1=cot35°+cot10°$

$\\\qquad\quad\displaystyle\sf{:}\implies cot10°.cot35°-cot35°-cot10°=1$

$\\\qquad\quad\displaystyle\sf{:}\implies cot10°.cot35°-cot35°-cot10°+1=2$

$\\\qquad\quad\displaystyle\sf{:}\implies cot35°(cot10°-1)-1 (cot10°-1)=2$

$\\\qquad\quad\displaystyle\sf{:}\implies (cot10°-1)(cot35°-1)=2$