Question

sin^2 70°+ cos^2 110° = 1​

Answer 1

SOLUTION

TO PROVE

$\sf{ { \sin}^{2} {70}^{ \circ} + { \cos}^{2} {110}^{ \circ} = 1 \: }$

EVALUATION

$\sf{ { \sin}^{2} {70}^{ \circ} + { \cos}^{2} {110}^{ \circ} \: }$

$= \sf{ { \sin}^{2} {70}^{ \circ} + { \big( \cos {110}^{ \circ} \big)}^{2} \: }$

$= \sf{ { \sin}^{2} {70}^{ \circ} + { \bigg[ \cos ( {180}^{ \circ} - {70}^{ \circ}) \bigg] }^{2} \: }$

$= \sf{ { \sin}^{2} {70}^{ \circ} + { \bigg[ \cos ( 2 \times {90}^{ \circ} - {70}^{ \circ}) \bigg] }^{2} \: }$

$= \sf{ { \sin}^{2} {70}^{ \circ} + { \bigg[ - \cos {70}^{ \circ} \bigg] }^{2} \: }$

$= \sf{ { \sin}^{2} {70}^{ \circ} + { \cos}^{2} {70}^{ \circ} \: }$

$= \sf{1 \: \: \: \: \: ( \: \because { \sin}^{2} \theta + { \cos}^{2} \theta \: = 1 \: )}$

Hence proved

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