81. If α + β = 90°, then the value of (1 - sin2α)(1 - cos2α) × (1 + cot2β)(1 + tan2β) is?
82. If $${\text{tan }}{9^ \circ } = \frac{p}{q}{\text{,}}$$ then the value of $$\frac{{{\text{se}}{{\text{c}}^2}{\text{8}}{{\text{1}}^ \circ }}}{{1 + {{\cot }^2}{{81}^ \circ }}}$$ is?
83. The value of following is, cos24° + cos55° + cos125° + cos204° + cos300° ?
84. If 7sin2θ + 3cos2θ = 4, (0° ≤ θ ≤ 90°), then the value of θ is?
85. If tan(2θ + 45°) = cot3θ, where (2θ + 45°) and 3θ are acute angles, then the value of θ is?
86. In sin(A - B) = $$\frac{1}{2}$$ and cos(A + B) =$$\frac{1}{2}$$ where A > B > 0 and A + B is an acute angle, then the value of B is?
87. sin2θ - 3sinθ + 2 = 0, will be true if ?
88. If 2(cos2θ - sin2θ) = 1, (θ is positive acute angle), then cotθ is equal to?
89. If $$\sin \alpha + \cos \beta = 2;$$ $$\left( {{0^ \circ } \leqslant \beta < \alpha \leqslant {{90}^ \circ }} \right){\text{,}}$$ then $${\text{sin}}\,{\left( {\frac{{2\alpha + \beta }}{3}} \right)^ \circ }$$ is?
90. If $$2\sin \left( {\frac{{\pi x}}{2}} \right) = {x^2} + \frac{1}{{{x^2}}}{\text{,}}$$ then the value of $$\left( {x - \frac{1}{x}} \right)$$ is?
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