91.
If x = 8(sinθ + cosθ) and y = 9(sinθ - cosθ), then the value of $$\frac{{{x^2}}}{{{8^2}}} + \frac{{{y^2}}}{{{9^2}}}$$  is:

92.
The value of $$\frac{{\left( {\cos {9^ \circ } + \sin {{81}^ \circ }} \right)\left( {\sec {9^ \circ } + {\text{cosec}}\,{\text{8}}{{\text{1}}^ \circ }} \right)}}{{{\text{cose}}{{\text{c}}^2}71 + {{\cos }^2}{{15}^ \circ } - {{\tan }^2}{{19}^ \circ } + {{\cos }^2}{{75}^ \circ }}}{\text{is:}}$$

93.
If tanθ + secθ = $$\frac{{x - 2}}{{x + 2}},$$  then what is the value of cosθ?

94.
If cosA + cosB + cosC = 3, then what is the value of sinA + sinB + sinC?

95.
Simplify the following: $$\frac{{\cos x - \sqrt 3 \sin x}}{2}$$

96.
Let 0° < θ < 90°, (1 + cot2θ)(1 + tan2θ) × (sinθ - cosecθ)(cosθ - secθ) is equal to:

97.
The expression $$\frac{{\left( {1 - 2{{\sin }^2}\theta {{\cos }^2}\theta } \right)\left( {\cot \theta + 1} \right)\cos \theta }}{{\left( {{{\sin }^4}\theta + {{\cos }^4}\theta } \right)\left( {1 + \tan \theta } \right){\text{cosec}}\,\theta }} - 1,$$       0° < θ < 90°, equals:

98.
If a = 45° and b = 15°, what is the value of $$\frac{{\cos \left( {a - b} \right) - \cos \left( {a + b} \right)}}{{\cos \left( {a - b} \right) + \cos \left( {a + b} \right)}}?$$

99.
What is the value of $$\cos \left( { - \frac{{17\pi }}{3}} \right)?$$

100.
What is the value of $$\frac{{\left[ {1 - \tan \left( {90 - \theta } \right) + \sec \left( {90 - \theta } \right)} \right]}}{{\left[ {\tan \left( {90 - \theta } \right) - \sec \left( {90 - \theta } \right) + 1} \right]}}?$$

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