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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
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