Find the value of $s i n^{2} 135^{o} + s e c^{2} 135^{o}$ .

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Solution

$sin 135^{o} = s i n (180^{o} - 45^{o}) = sin 45^{o} = \frac{1}{\sqrt{2}}$

$sec 135^{o} = s e c (180^{o} - 45^{o}) = - sec 45^{o} = - \sqrt{2}$

Therefore, required value is $\frac{1}{2} + 2 = \frac{5}{2}$ .

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