InterviewSolution
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InterviewSolution
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The value of \(\frac{{\left[ {4co{s^4}32^\circ cose{c^2}58^\circ - sin63^\circ cos27^\circ - co{s^2}63^\circ \; + \;1} \right]}}{{\left[ { - cose{c^2}24^\circ \; + \;ta{n^2}66^\circ - se{c^2}31^\circ \; + \;co{t^2}59^\circ } \right]{{\cos }^2}32}}\) is –1. 12. -13. 24. -2 |
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Answer» Correct Answer - Option 4 : -2 GIVEN: \(\frac{{\left[ {4co{s^4}32^\circ cose{c^2}58^\circ - sin63^\circ cos27^\circ - co{s^2}63^\circ \; + \;1} \right]}}{{\left[ { - cose{c^2}24^\circ \; + \;ta{n^2}66^\circ - se{c^2}31^\circ \; + \;co{t^2}59^\circ } \right]{{\cos }^2}32^\circ }}\) FORMULA USED: sin(90° - x) = cos x, cosec(90° - x) = sec x (1 – sin2x) = cos2x (1 – cos2x) = sin2x CALCULATION: \(\frac{{\left[ {4co{s^4}32^\circ cose{c^2}58^\circ - sin63^\circ cos27^\circ - co{s^2}63^\circ \; + \;1} \right]}}{{\left[ { - cose{c^2}24^\circ \; + \;ta{n^2}66^\circ - se{c^2}31^\circ \; + \;co{t^2}59^\circ } \right]\;{{\cos }^2}32^\circ }}\) = \(\frac{{\left[ {4co{s^4}32^\circ se{c^2}32^\circ - sin63^\circ sin63^\circ - co{s^2}63^\circ \; + \;1} \right]}}{{\left[ { - se{c^2}66^\circ \; + \;ta{n^2}66^\circ - cose{c^2}59^\circ \; + \;co{t^2}59^\circ } \right]\;{{\cos }^2}32^\circ }}\) = \(\frac{{\left[ {4co{s^2}32^\circ - {{\sin }^2}63^\circ - co{s^2}63^\circ \; + \;1} \right]}}{{\left[ { - se{c^2}66^\circ \; + \;ta{n^2}66^\circ - cose{c^2}59^\circ \; + \;co{t^2}59^\circ } \right]\;{{\cos }^2}32^\circ }}\) = \(\frac{{\left[ {4co{s^2}32^\circ } \right]}}{{\left[ { - 1 - 1} \right]{{\cos }^2}32^\circ }}\) = 4/(- 2) = - 2 |
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