Question

Prove that sin 55 °- cos 35°= 0.​

Answer 1

$\large\underline{\sf{Solution-}}$

We know that

$\: \: \: \: \boxed{ \bf{ \: sin(90 \degree \: - x) = cosx}}$

Now,

Consider,

$\rm :\longmapsto\:sin55 \degree \: - \: cos35\degree$

$\rm :\longmapsto\: = \: sin(90\degree - \: 35\degree) - cos35\degree$

$\rm :\longmapsto\: = \: cos35\degree \: - \: cos35\degree$

$\rm :\longmapsto\: = \: 0$

${\boxed{\boxed{\bf{Hence, Proved}}}}$

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Additional Information :-

$\boxed{ \bf{ \: cos(90 \degree \: - x) = sinx}}$

$\boxed{ \bf{ \: tan(90 \degree \: - x) = cotx}}$

$\boxed{ \bf{ \: cot(90 \degree \: - x) = tanx}}$

$\boxed{ \bf{ \: sec(90 \degree \: - x) = cosecx}}$

$\boxed{ \bf{ \: cosec(90 \degree \: - x) = secx}}$