2(cos^2 73° + cos^2 47°) - cos 154°
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Answers
Answer:
2
Step-by-step explanation:
let A=73 degree and B=47 degree
we find that , 154=180-(73-47) in terms of degree
Expression is now,
=2( cos^2 A + cos^2 B ) - cos [ pi - (A - B) ]
= 2cos^2A +2cos^2B + cos(A - B) [ using cos (pi-X) = - cosX ]
So,
=2cos^2A +2cos^2B + cos(A - B)
= (2 cos^2A - 1) + (2 cos^2B - 1) + cos(A - B) +2
= cos 2A + cos 2B + cos(A - B) +2
= cos146 + cos94 + cos26 +2
Now,
=[cos 146 + cos 94 ] = 2cos120 * cos26 { cosC+cosD = 2cos(C+D)/2*cos(C-D)/2 }
So now expression,
= 2cos120 * cos26 + cos26 + 2
= 2(-1/2)*cos26+cos26+2 we know cos 120 = - cos 60 = -1/2
= -cos26+cos26+2 = 2.
i hope you understand...just go with the formulas
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Answer:
The value of 2(cos^2 73° + cos^2 47°) - cos 154° is '2'.
Step-by-step explanation:
Consider
2(cos^2 73° + cos^2 47°) - cos 154°
= 2cos^2 73°+ 2cos^247° - cos 154°
Add 2 and subtract 2 from the above
= (2cos^2 73°-1) + (2cos^247°- 1) + 2 - cos(180° - 26°)
= cos2(73°) + cos2(47°) + 2 - cos(180° - 26°) [since 2cos^2A-1=cos2A]
= (cos 146° + cos 94°) + 2 -(-cos 26°) [since, cos(180° - θ) = -cosθ]
= 2 cos ((146 + 94)/2)cos ((146 - 94)/2) + 2 + cos 26°
[since, cosA+cosB = 2cos((A+B)/2)cos((A-B)/2)]
= 2cos120° cos 26° + 2 + cos 26°
= 2(-1/2) cos26° + 2 + cos 26° [since cos120° = -1/2]
= 2 + (-1)cos26° + cos26°
= 2 + 0
= 2
Hence the value of 2(cos^2 73° + cos^2 47°) - cos 154° = 2
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