Question

Mă autoizolez dacă imi rezolva cineva asta (F), promit.​

Answer 1

sin(23π/4)=sin(24π/4–π/4)=sin(6π–π/4)

=sin(–π/4)=sin(–π/4)=-sin(π/4)=- √2/2

tg(37π/4)=tg(36π/4+π/4)= tg(9π+π/4)

=tg(π/4)=1

ctg(-π/4)= -ctg(π/4)=-1

F=2sin² (23π/4)+tg²(37π/4)•ctg(-π/4)

F=2•(- √2/2) ²+1²•(-1)

F=2•2/4-1=1-1

F=0

Answer 2

Răspuns:

$sin\dfrac{23\pi }{4} =sin\dfrac{24\pi -\pi }{4} =sin(\dfrac{24\pi }{4}-\dfrac{\pi }{4})=sin(2\pi*3-\dfrac{\pi }{4})=sin(-\dfrac{\pi }{4})=-sin\dfrac{\pi }{4}=-\dfrac{\sqrt{2} }{2}.~~Deci~sin^{2} \dfrac{23\pi }{4} =(-\dfrac{\sqrt{2} }{2})^{2}=\dfrac{2}{4}=\dfrac{1}{2}.$

$tg\dfrac{37\pi }{4}= tg\dfrac{36\pi+\pi }{4}=tg(9\pi +\dfrac{\pi }{4} )=tg\dfrac{\pi }{4}=1.\\Deci~tg^{2}\dfrac{37\pi }{4}=1;~~~ctg(-\dfrac{\pi }{4})=-ctg(\dfrac{\pi }{4})=-1$

Atunci F=2·(1/2)+1·(-1)=1-1=0.

Explicație pas cu pas: