Find the value of $3tan^{2} 26^{o} -3cosec^{2} 64^{o}$.

Given:  The expression $3tan^{2} 26^{o} -3cosec^{2} 64^{o}$

To do: Find the value of  the expression.

Solution:

$3tan^{2} 26^{o} -3cosec^{2} 64^{o}$.

$tan(26°)=cot(90-26) = cot(64°)$

So, $3tan^2(26^{o})=3cot^2(64^{o})$

= $3tan^2(26^{o})–3cosec^2(64^{o})$ can be written as

=$3cot^2(64^{o})–3cosec^2(64^{o})$

= $3[cot^2(64^{o})–cosec^2(64^{o})]$

= $3(-1) = -3$ [Using $cosec^2 - cot^2=1$]

Therefore, the value of $3tan^{2} 26^{o} -3cosec^{2} 64^{o}$. is -3