Question

what is the value of cos^2 31-sin^2 59​

Answer 1

Step-by-step explanation:

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Jai hind

Answer 2

SOLUTION

TO DETERMINE

$\sf{ { \cos}^{2} {31}^{ \circ} - { \sin}^{2} {59}^{ \circ} \: }$

FORMULA TO BE IMPLEMENTED

We are aware of the Trigonometric identity that

$\sf{ \sin( {90}^{ \circ} - \theta) = \cos \theta}$

EVALUATION

$\sf{ { \cos}^{2} {31}^{ \circ} - { \sin}^{2} {59}^{ \circ} \: }$

$= \sf{ { \cos}^{2} {31}^{ \circ} - {\big({ \sin} {59}^{ \circ} \big)}^{2} \: }$

$= \sf{ { \cos}^{2} {31}^{ \circ} - {\bigg[{ \sin}({90}^{ \circ} - {31}^{ \circ}) \bigg]}^{2} \: }$

$= \sf{ { \cos}^{2} {31}^{ \circ} - {\big({ \cos} {31}^{ \circ} \big)}^{2} \: }$

$= \sf{ { \cos}^{2} {31}^{ \circ} - { \cos}^{2} {31}^{ \circ}\: }$

$= \sf{0 \: }$

FINAL ANSWER

$\boxed{ \sf{ \: { \cos}^{2} {31}^{ \circ} - { \sin}^{2} {59}^{ \circ} = 0 \: }}$

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