Question

tan70°⋅tan65°−tan70°−tan65°=1 prove that

Answer 1

$\textbf{To Prove:}$

$tan\,70^{\circ}\,tan\,65^{\circ}-tan\,70^{\circ}-tan\,65^{\circ}=1$

$\textbf{Solution:}$

$\text{Consider,}$

$tan\,135^{\circ}$

$tan\,135^{\circ}=tan(70^{\circ}+65^{\circ})$

$\text{Using the following identity}$

$\boxed{\bf\,tan(A+B)=\frac{tanA+tanB}{1-tanA\,tanB}}$

$-1=\dfrac{tan\,70^{\circ}+tan\,65^{\circ}}{1-tan\,70^{\circ}\;tan\,65^{\circ}}$

$-1(1-tan\,70^{\circ}\;tan\,65^{\circ})=tan\,70^{\circ}+tan\,65^{\circ}$

$-1+tan\,70^{\circ}\;tan\,65^{\circ}=tan\,70^{\circ}+tan\,65^{\circ}$

$\text{Rearranging terms we get}$

$tan\,70^{\circ}\;tan\,65^{\circ}-tan\,70^{\circ}-tan\,65^{\circ}=1$

$\therefore\bf\,tan\,70^{\circ}\;tan\,65^{\circ}-tan\,70^{\circ}-tan\,65^{\circ}=1$

Find more:

7tan(a-b)=5tan(a+b) then find the value of sin2a\sin2b​

https://brainly.in/question/16800034

यदि A+B+C= 90 तो सिद्ध कीजिए: tanAtanB+tanBtanC+tanCtanA=1

https://brainly.in/question/15268179

Tan 25 tan 31 + tan 31 tan 34 + tan 34 + yan 25

https://brainly.in/question/11539067

Tan8a-tan5a-tan3a show that tan8a.tan5a.tan3a

https://brainly.in/question/5758781