Question

cos225-sin225+tan495-cot495

Answer 1

ANSWER ;


Dear Student,

Please find below the solution to the asked query :

cos 225 − sin 225 + tan 495 − cot 495=cos(180+45) − sin(180+45) + tan(360+135) − cot(360+135)=− cos 45 − (− sin 45) + tan 135 − cot 135=− cos 45 + sin 45 + tan(90+45) − cot(90+45)=− cos 45 + sin 45 − tan 45 − (− cot 45)=−12√ + 12√ − 1 + 1=0

Hope this would clear your doubt.

...................... OR...........................
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cos 225 degrees=cos(180+45) degrees=-cos 45 degrees
Likewise
sin 225 degrees = -sin 45 degrees
tan 495 degrees = tan(360+135) degrees = tan (180-45) degrees= - tan 45 degrees
Likewise cot 495 degrees = -cot 45 degrees
sin 45 degrees = 1/square root of 2=cos 45 degrees
and

cos20 cos40 cos60 cos80= 1/16

l.h.s. :

cos20 cos40 1/2 cos80 (cos60 = 1/2)

multiply nd divide by 2

1/4 (2 cos20 cos40 cos80)

1/4 (cos(20+80)+ cos(20-80)) cos40  (2cosa cosb= cos(a+b) + cos(a-b))

1/4 (cos(-60)+ cos(100)) cos40

1/4(1/2 + cos100)cos40

1/8 cos40+ 1/4 (cos40 cos100)

multiplt nd divide by 2

2/2(1/8 cos40) + 1/8(2 cos40 cos100)

1/8 cos40+ 1/8 (cos140+ cos(-60))  (2cosa cosb= cos(a+b) cos(a-b))

1/8 cos40+ 1/8 cos140 + 1/16  (cos60= 1/2)

1/8(cos40+cos140) + 1/16

1/8(2 cos90 cos(-50)) + 1/16  (as above identity)

cos90= 0

1/16

= r.h.s

hence proved......

Answer 2

Answer:

evaluate cos225°-sin225°+tan495°-cot495°