if 2 cos 2x =1, then x is equal to :
Answers
Answered by
1
Answer:
30°
Step-by-step explanation:
cos 2x = 1/2
2x=60°
x=30°
Answered by
1
cos2x+2cosx=1
2cos
2
x−1+2cosx=1(∵cos2x=2cos
2
x−1)
⇒2cos
2
x+2cosx−2=0
⇒cos
2
x+cosx=1.....(1)
⇒1−cos
2
x=cosx
⇒sin
2
x=cosx.....(2)
Now,
sin
2
(2−cos
2
x)
=sin
2
x(1+sin
2
x)
=cosx(1+cosx)[From(2)]
=cosx+cos
2
x
=1[From(1)]
Hence sin
2
(2−cos
2
x)=1.
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2cos
2
x−1+2cosx=1(∵cos2x=2cos
2
x−1)
⇒2cos
2
x+2cosx−2=0
⇒cos
2
x+cosx=1.....(1)
⇒1−cos
2
x=cosx
⇒sin
2
x=cosx.....(2)
Now,
sin
2
(2−cos
2
x)
=sin
2
x(1+sin
2
x)
=cosx(1+cosx)[From(2)]
=cosx+cos
2
x
=1[From(1)]
Hence sin
2
(2−cos
2
x)=1.
Mark as brainlist
And please thank my answer
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