Question

Evaluate tan 26°. tan 64​

Answer 1

$\mathtt{\bf{\large{\underline {\red{Given \: question}}}}}$

Evaluate :

$\sf {tan26° \times tan64° }$

$\mathtt{\sf{\large{\underline {\red{Required \: answer}}}}}$

$\huge \mathcal \color{red}{1}$

$\sf\huge\color{orange}{\underline{\underline {Solution}}}$

$\sf\color{pink}{Given, }$

$\sf{tan26° \times tan64° }$

$\sf tan26° \:c an \: also \: \: written \: as:- \\ ⟹ tan(90 - 64)°$

$\sf\color{purple}{We\: know, }$

$\sf{ tan \: (90 -θ ) = cotθ }$

$\sf\color{purple}{Here, \: θ = \:64°}$

$\color{pink}{and}$

$\sf cotθ \times tanθ = 1$

$\color{pink}{So,}$

$\sf tan(90 - 64)° \times tan(64)° \\ ⟹ cot64° \times tan64° \\ ⟹ 1$

$\sf\color{pink}{\underline{\underline {Formula \: used:-}}}$

$\sf☞ \: tan \: (90 -θ ) = cotθ$

$\sf☞ \: cotθ \: \times \: tanθ = 1$

▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬

Answer 2

We know that tan theta = 90-cot theta so tan 26*cot 26 so it is undefined as tan 90 is undefined