Question

tan squre 120° cot squre 240° - cot squre 210° tan squre 240°/ 3tan 45° sin 270° - sec 360° cos270°​

Answer 1

SOLUTION

TO EVALUATE

$\displaystyle \sf{ { \tan}^{2} {120}^{ \circ} { \cot}^{2} {240}^{ \circ} - \frac{ { \cot}^{2} {210}^{ \circ} { \tan}^{2} {240}^{ \circ}}{3 \tan {45}^{ \circ} \sin {270}^{ \circ} } - 4 \sec {360}^{ \circ} \cos {270}^{ \circ} }$

EVALUATION

$\displaystyle \sf{ { \tan}^{2} {120}^{ \circ} { \cot}^{2} {240}^{ \circ} - \frac{ { \cot}^{2} {210}^{ \circ} { \tan}^{2} {240}^{ \circ}}{3 \tan {45}^{ \circ} \sin {270}^{ \circ} } - 4 \sec {360}^{ \circ} \cos {270}^{ \circ} }$

$\displaystyle \sf{ = { \tan}^{2}( 2 \times {90}^{ \circ} -{60}^{ \circ} ) { \cot}^{2} (3 \times {90}^{ \circ} -{30}^{ \circ} ) - \frac{ { \cot}^{2}( 2 \times {90}^{ \circ} + {30}^{ \circ} ){ \tan}^{2} (3 \times {90}^{ \circ} - {30}^{ \circ} )}{3 \tan {45}^{ \circ} \sin (3 \times {90}^{ \circ} + {0}^{ \circ} )} - 4 \sec (4 \times {90}^{ \circ} + {0}^{ \circ} ) \cos (3 \times {90}^{ \circ} + {0}^{ \circ} ) }$

$\displaystyle \sf{ = { \tan}^{2}{60}^{ \circ} { \tan}^{2} {30}^{ \circ} - \frac{ { \cot}^{2} {30}^{ \circ} { \cot}^{2} {30}^{ \circ} }{3 \tan {45}^{ \circ} \times - \cos {0}^{ \circ} } - 4 \sec {0}^{ \circ} \sin {0}^{ \circ} }$

$\displaystyle \sf{ = 3 \times \frac{1}{3} + \frac{ 3 \times 3 }{3 \times 1 \times 1} - 4 \times 1 \times 0}$

$= 1 + 3$

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