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The value of $$\frac{{3\left( {{{\cot }^2}{{47}^ \circ } - {{\sec }^2}{{43}^ \circ }} \right) - 2\left( {{{\tan }^2}{{23}^ \circ } - {\text{cose}}{{\text{c}}^2}{{67}^ \circ }} \right)}}{{{\text{cose}}{{\text{c}}^2}\left( {{{68}^ \circ } + \theta } \right) - \tan \left( {\theta + {{61}^ \circ }} \right) - {{\tan }^2}\left( {{{22}^ \circ } - \theta } \right) + \cot \left( {{{29}^ \circ } - \theta } \right)}}\,{\text{is:}}$$

The value of $$\frac{{3\left( {{{\cot }^2}{{47}^ \circ } - {{\sec }^2}{{43}^ \circ }} \right) - 2\left( {{{\tan }^2}{{23}^ \circ } - {\text{cose}}{{\text{c}}^2}{{67}^ \circ }} \right)}}{{{\text{cose}}{{\text{c}}^2}\left( {{{68}^ \circ } + \theta } \right) - \tan \left( {\theta + {{61}^ \circ }} \right) - {{\tan }^2}\left( {{{22}^ \circ } - \theta } \right) + \cot \left( {{{29}^ \circ } - \theta } \right)}}\,{\text{is:}}$$ Correct Answer -1

$$\eqalign{ & \frac{{3\left( {{{\cot }^2}{{47}^ \circ } - {{\sec }^2}{{43}^ \circ }} \right) - 2\left( {{{\tan }^2}{{23}^ \circ } - {\text{cose}}{{\text{c}}^2}{{67}^ \circ }} \right)}}{{{\text{cose}}{{\text{c}}^2}\left( {{{68}^ \circ } + \theta } \right) - \tan \left( {\theta + {{61}^ \circ }} \right) - {{\tan }^2}\left( {{{22}^ \circ } - \theta } \right) + \cot \left( {{{29}^ \circ } - \theta } \right)}} \cr & = \frac{{3\left( {{{\tan }^2}{{43}^ \circ } - {{\sec }^2}{{43}^ \circ }} \right) - 2\left( {{{\tan }^2}{{23}^ \circ } - {{\sec }^2}{{23}^ \circ }} \right)}}{{{\text{cose}}{{\text{c}}^2}\left( {{{68}^ \circ } + \theta } \right) - \tan \left( {\theta + {{61}^ \circ }} \right) - {{\cot }^2}\left( {{{68}^ \circ } - \theta } \right) + \tan \left( {{{61}^ \circ } - \theta } \right)}} \cr & = \frac{{3 \times \left( { - 1} \right) - 2 \times \left( { - 1} \right)}}{1} \cr & = \frac{{ - 3 + 2}}{1} \cr & = - 1 \cr} $$

Related Questions

What is the value of \(\frac{{cosec\;\left( {78^\circ - \theta } \right) - \sec \left( {12^\circ \; + \;\theta } \right) - \tan \left( {67^\circ \; + \;\theta } \right)\; + \;\cot \left( {23^\circ - \theta } \right)}}{{\tan 13^\circ \tan 37^\circ \tan 45^\circ \tan 53^\circ \tan 77^\circ }}?\)
The value of $$\frac{{3\left( {{\text{cose}}{{\text{c}}^2}{{26}^ \circ } - {{\tan }^2}{{64}^ \circ }} \right) + \left( {{{\cot }^2}{{42}^ \circ } - {{\sec }^2}{{48}^ \circ }} \right)}}{{\cot \left( {{{22}^ \circ } - \theta } \right) - {\text{cose}}{{\text{c}}^2}\left( {{{62}^ \circ } + \theta } \right) - \tan \left( {\theta + {{68}^ \circ }} \right) + {{\tan }^2}\left( {{{28}^ \circ } - \theta } \right)}}\,{\text{is:}}$$
The value of $$\frac{{\sec \theta \left( {1 - \sin \theta } \right)\left( {\sin \theta + \cos \theta } \right)\left( {\sec \theta + \tan \theta } \right)}}{{\sin \theta \left( {1 + \tan \theta } \right) + \cos \theta \left( {1 + \cot \theta } \right)}}$$        is equal to:
The value of $$\frac{{4{{\tan }^2}{{30}^ \circ } + {{\sin }^2}{{30}^ \circ }{{\cos }^2}{{45}^ \circ } + {{\sec }^2}{{48}^ \circ } - {{\cot }^2}{{42}^ \circ }}}{{\cos {{37}^ \circ }\sin {{53}^ \circ } + \sin {{37}^ \circ }\cos {{53}^ \circ } + \tan {{18}^ \circ }\tan {{72}^ \circ }}}\,{\text{is:}}$$
$$\frac{{2{\text{sin }}{{68}^ \circ }}}{{{\text{cos 2}}{{\text{2}}^ \circ }}}$$   $$ - $$ $$\frac{{2{\text{cot 1}}{5^ \circ }}}{{5\tan {{75}^ \circ }}}$$   $$ - $$ $$\frac{{3\tan {{45}^ \circ }.\tan {{20}^ \circ }.\tan {{40}^ \circ }.\tan {{50}^ \circ }.\tan {{70}^ \circ }}}{5}$$         is equal to?
The value of the following is : $$\frac{{{{\left( {\tan {{20}^ \circ }} \right)}^2}}}{{{{\left( {{\text{cosec 7}}{0^ \circ }} \right)}^2}}}$$   $$ + $$ $$\frac{{{{\left( {\cot {{20}^ \circ }} \right)}^2}}}{{{{\left( {{\text{sec 7}}{0^ \circ }} \right)}^2}}}$$   $$ + $$ $$2\tan {15^ \circ }$$ . $$\tan {45^ \circ }$$ . $$\tan {75^ \circ }$$
The expression $$\frac{{{{\left( {1 - \sin \theta + \cos \theta } \right)}^2}\left( {1 - \cos \theta } \right){{\sec }^3}\theta \,{\text{cose}}{{\text{c}}^2}\theta }}{{\left( {\sec \theta - \tan \theta } \right)\left( {\tan \theta + \cot \theta } \right)}},$$        0°
$$\frac{{{{\left( {1 + \sec \theta \,{\text{cosec}}\,\theta } \right)}^2}{{\left( {\sec \theta - \tan \theta } \right)}^2}\left( {1 + \sin \theta } \right)}}{{{{\left( {\sin \theta + \sec \theta } \right)}^2} + {{\left( {\cos \theta + {\text{cosec}}\,\theta } \right)}^2}}},$$        0°
If $$\frac{{\sec \theta - \tan \theta }}{{\sec \theta + \tan \theta }} = \frac{1}{7},\,\theta ,$$     lies in first quadrant, then the value of $$\frac{{{\text{cosec}}\,\theta + {{\cot }^2}\theta }}{{{\text{cosec}}\,\theta - {{\cot }^2}\theta }}$$   is:
The value of $$\frac{{\sin \left( {{{78}^ \circ } + \theta } \right) - \cos \left( {{{12}^ \circ } - \theta } \right) + \left( {{{\tan }^2}{{70}^ \circ } - {\text{cose}}{{\text{c}}^2}{{20}^ \circ }} \right)}}{{\sin {{25}^ \circ }\cos {{65}^ \circ } + \cos {{25}^ \circ }\sin {{65}^ \circ }}}{\text{ is:}}$$