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شائع علم المثلثات >

sin(arcsin(1)+arccos(1))

الحلّ

sin (arcsin (1) + arccos (1))

الحلّ

1

خطوات الحلّ

sin (arcsin (1) + arccos (1))

Rewrite using trig identities:

sin (arcsin (1)) cos (arccos (1)) + cos (arcsin (1)) sin (arccos (1))

sin (arcsin (1) + arccos (1))

sin (s + t) = sin (s) cos (t) + cos (s) sin (t)

:فعّل متطابقة الجمع لزوايا

= sin (arcsin (1)) cos (arccos (1)) + cos (arcsin (1)) sin (arccos (1))

= sin (arcsin (1)) cos (arccos (1)) + cos (arcsin (1)) sin (arccos (1))

Rewrite using trig identities:

sin (arcsin (1)) = 1

sin (arcsin (x)) = x :

استخدم المتطابقة التالية

= 1

Rewrite using trig identities:

cos (arccos (1)) = 1

cos (arccos (x)) = x :

استخدم المتطابقة التالية

= 1

Rewrite using trig identities:

cos (arcsin (1)) = 0

cos (arcsin (1))

Rewrite using trig identities:

cos (arcsin (1)) = 1 - 1^{2}

cos (arcsin (x)) = 1 - x^{2} :

استخدم المتطابقة التالية

= 1 - 1^{2}

= 1 - 1^{2}

بسّط

= 0

Rewrite using trig identities:

sin (arccos (1)) = 0

sin (arccos (1))

Rewrite using trig identities:

sin (arccos (1)) = 1 - 1^{2}

sin (arccos (x)) = 1 - x^{2} :

استخدم المتطابقة التالية

= 1 - 1^{2}

= 1 - 1^{2}

بسّط

= 0

= 1 \cdot 1 + 0 \cdot 0

بسّط

= 1

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