(sin (-660°) tan (1050°) sec (-420°))/
(cos (225°) cosec (315º) cos (510°))
options:
1)√3/4
2) √3/2
3) 2/√3
4) 4/√3
Answers
Step-by-step explanation:
To solve this question you must know about the trigonometry quadrant concept
sin(−660)=−sin(90×7+30)=cos30=3–√2
tan(1050)=tan(90×11+60)=−cot60=13–√
sec(−420)=sec(90×4+60)=sec60=2
cos(225)=cos(90×2+45)=−cos45=−12–√
cosec(315)=cosec(90×3+45)=−sec45=−2–√
cos(510)=cos(90×5+60)=−sin60=−3–√2
Now put all the values
3–√2×−13–√×2−12–√×(−2–√)×3–√−2
23–√
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Let us assume that the solution is S. Then,
S=sin(−660)tan(1050)sec(−420)(cos225)(cosec315)(cos510)
We make the following changes:
sec x=1/cosx
Sec(-420) = [(1/cos(-420)]
cosec x =1 / sin x
Cosec(315) = [(1/sin(315)]
Thus, S=sin(−660)tan(1050)sin(315)cos(225)cos(−420)cos(510)
Now,
sin (-x) = - sin x
sin (-660) = - sin 660
Cos (-x) = cos x
Cos (-420) = cos 420
Thus, S=−sin(660)tan(1050)sin(315)cos(225)cos(420)cos(510)
We further use the identities:
Sin (2π + x ) = sin x
Sin (660) = sin ( 360 + 300) = sin ( 2π + 300) = sin (300)
Sin ( π + x) = - sin x
Sin (300) = sin ( 180 + 120) = sin
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